Question

A diver leaves the end of a 4.0 m high diving board and strikes the water...

A diver leaves the end of a 4.0 m high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Ignoring the height of the diver (assume she is a particle), determine: a) her initial velocity and angle at which she jumped, b) her maximum height reached, and c) the velocity and angle with which she enters the water.

Homework Answers

Answer #1

Let us consider:

u be the initial velocity of thee diver
x be the horizontal distance from the end of the diving board,
y0 be the initial height above water,
t be the time from take-off until entering the water,
g be the acceleration due to gravity,
a be the diver's angle to the horizontal at the time of take-off,
v be the diver's speed of entry into the water,
b be the angle of entry measured from the horizontal.

(a) 0 = y0 + ut sin(a) - gt^2 / 2 ...(1)
x = ut cos(a) ...(2)

From (1):
ut sin(a) = - y0 + gt^2 / 2 ...(3)

Sqaring (3) and adding to (2):
u^2 t^2 = x^2 + (gt^2 / 2- y0)^2
u^2 = [ x^2 + (gt^2 / 2 - y0)^2 ] / t^2
u = sqrt[ x^2 + (gt^2 / 2 - y0)^2 ] / t

y0 = 4.0 m
t = 1.3 s
x = 3.0 m
g = 9.81 m/s^2

Hence, u = sqrt[ 9.0 + (8.289 - 4.0)^2 ] / 1.3 = 4.02 m/s

From (2):
cos(a) = x / (ut) = 3/4.02*1.3 =0.574
a = 54.97 deg.

(b) As the vertical velocity at the highest point is 0:
0 = [ u sin(a) ]^2 - 2g(y - y0)
y = y0 + [ u sin(a) ]^2 / (2g)
= 4.0 + 0.552 = 4.552 m.

(c) v sin(b) = u sin(a) - gt ...(4)
v cos(b) = u cos(a) ...(5)

Squaring and adding (4) and (5):
v^2 = u^2 - 2ugt sin(a) + (gt)^2
v = [4.02^2 - 2*4.02*9.81*1.3*0.82 + (9.81*1.3)^2]^1/2

= [16.16 - 84.078 + 162.64]^1/2 = 9.73 m/s

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A high diver leaves the end of a 6.0 m high diving board and strikes the...
A high diver leaves the end of a 6.0 m high diving board and strikes the water 1.2 s later, 2.0 m beyond the end of the board. Considering the diver as a particle, Part A Determine the magnitude of her initial velocity, v⃗ 0. Part B Determine the angle of her initial velocity, v⃗ 0. Part C Determine the maximum height reached Part D Determine the magnitude of the velocity v⃗ f with which she enters the water ....
A high diver leaves the end of a 6.0 m high diving board and strikes the...
A high diver leaves the end of a 6.0 m high diving board and strikes the water 1.4 s later, 4.0 mbeyond the end of the board. Considering the diver as a particle, Determine the magnitude of her initial velocity, v⃗ 0. Express your answer to two significant figures and include the appropriate units. Determine the angle of her initial velocity, v⃗ 0. Express your answer to two significant figures and include the appropriate units. Determine the maximum height reached....
A 55-kg diver stands at the end of a diving board located 10 m above the...
A 55-kg diver stands at the end of a diving board located 10 m above the water level. The diving board is held down at one end by an anchor bolt. The fulcrum is located at 1.4 m from the bolt and the total length of the board is 3.9 m. Draw a free body diagram showing the forces acting on the diver. Calculate the torque that she exerts on the board with respect to the fulcrum. Neglect the mass...
A 55-kg diver stands at the end of a diving board located 10 m above the...
A 55-kg diver stands at the end of a diving board located 10 m above the water level. The diving board is held down at one end by an anchor bolt. The fulcrum is located at 1.4 m from the bolt and the total length of the board is 3.9 m.   a) Draw a free body diagram showing the forces acting on the diver. (b) Calculate the torque that she exerts on the board with respect to the fulcrum. Neglect...
Q2. A 55-kg diver stands at the end of a diving board located 10 m above...
Q2. A 55-kg diver stands at the end of a diving board located 10 m above the water level. The diving board is held down at one end by an anchor bolt. The fulcrum is located at 1.4 m from the bolt and the total length of the board is 3.9 m. (a) Draw a free body diagram showing the forces acting on the diver. (b) Calculate the torque that she exerts on the board with respect to the fulcrum....
A diver leaves a 3-m board on a trajectory that takes her 2.3 m above the...
A diver leaves a 3-m board on a trajectory that takes her 2.3 m above the board and then into the water 2.7 m horizontally from the end of the board. At what speed did she leave the board? At what angle did she leave the board?
A diver springs upward from a board that is 2.90 m above the water. At the...
A diver springs upward from a board that is 2.90 m above the water. At the instant she contacts the water her speed is 11.0 m/s and her body makes an angle of 62.7 ° with respect to the horizontal surface of the water. Determine her initial velocity, both (a) magnitude and (b) direction.
A diver springs upward from a board that is 2.84 meters above the water. At the...
A diver springs upward from a board that is 2.84 meters above the water. At the instant she contacts the water her speed is 8.67 m/s and her body makes an angle of 73.9° with respect to the horizontal surface of the water. Determine her initial velocity.
A diver springs upward from a board that is 3.01 meters above the water. At the...
A diver springs upward from a board that is 3.01 meters above the water. At the instant she contacts the water her speed is 9.37 m/s and her body makes an angle of 76.3° with respect to the horizontal surface of the water. Determine her initial velocity.
A diver springs upward from a board that is 3.20 meters above the water. At the...
A diver springs upward from a board that is 3.20 meters above the water. At the instant she contacts the water her speed is 8.75 m/s and her body makes an angle of 79.4° with respect to the horizontal surface of the water. Determine her initial velocity.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT
Active Questions
  • Determine the cumulative 15-year 18 kip ESAL’s in the design lane for 2-lane highway for the...
    asked 6 minutes ago
  • Q: Dr.Grimace, the evil dentist, is trying to find out if his patients suffer from periodontal...
    asked 6 minutes ago
  • After collecting data on 19283 dogs, you find that male vallhunds have an average weight of...
    asked 8 minutes ago
  • Research Target Corporation and assess your satisfaction with the company you researched and make recommendations about...
    asked 9 minutes ago
  • Evidence suggests that 70% of FSU students like turtles. Suppose we randomly sampled 15 FSU students....
    asked 9 minutes ago
  • Ulrich challenges the appropriateness of the nearly universal symbolism of the spinning wheel as the marker...
    asked 10 minutes ago
  • Differential Equations: Please try to computer type, if not possible be clear and organize. Thank you...
    asked 10 minutes ago
  • In your opinion, what are the three (3) most important benefits an employer can give to...
    asked 16 minutes ago
  • In a test of the effectiveness of garlic for lowering​ cholesterol, 81 subjects were treated with...
    asked 18 minutes ago
  • How does the 95% confidence interval correspond to the reported conclusion at a 0.05 significance level?...
    asked 19 minutes ago
  • 1) Consider the following Java program, which one of the following best describes "setFlavor"? public class...
    asked 19 minutes ago
  • You've had a chance to learn about Facebook, its model, growth, outlook, strategic assets, and competitive...
    asked 19 minutes ago