Question

Problem 3: While playing basketball, a batter hits the ball as it crosses home plate and gives it an initial velocity of 45m/s and launches it an angle of 19 degree above the horizontal (x-axis). The outfield wall is located 115m away from the home plate and is 3m high. The batter hits the ball when it is 1m above home pate.

Part A: Find the equation describing the position and velocity of the ball as function of the

Part B: Does the ball go over thew all fro a home run? Justify answer

Part C: A bird is flying at a constant height of 15m above the field while the ball is in the air. Is the bird in danger of begin hit by the ball?

Problem 2: A car is in a drag race where it accelerated from rest at 3m/s^2 until it reaches it maximum velocity. The race is 100m long.

Part A: If the car reaches its maximum velocity after 5 seconds, what is the cars maximum velocity.

Part B: How fat has the car travelled when it reaches it maximum velocity?

Part C: As the race is 100m long, how long does it take for the car to reach the finish line?

Answer 1

problem 2

a)

v = at = 3* 5 = 15 m/s

b)

d = 0.5 at^2 = 0.5* 1.5* 5^2 = 37.5 m

c)

t = (100 - 37.5) / 15 = 4.167

tital time taken by car

T = 5 + t = 9.167 s

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3.

a)

position is given by

y = ho + v sin x * t - 0.5 gt^2

y = 1 + 45 sin 19 t - 4.9 t^2

y = 1+ 14.61 t - 4.9 t^2

horizontal velocity

vx = 45 cos 19 = 42.55 m/s

vertical component of velocity

vy = 45 sin 19 - 9.8t =14.6 - 9.8 t

b)

time taken by ball to reach home run

t = 115 /42.55 = 2.703 s

vertical position

h = 1 + 14.6* 2.703 - 4.9* 2.703^2

h = 4.66 m

yes, the ball will clear the given height

c)

max height reached by the ball

H = 1 + 14.6^2 / 19.6 = 11.876 m

since bird height(15m) is greater than max height reached ( 11.876 m)

so bird will be safe

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