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?
v = at = 3* 5 = 15 m/s
d = 0.5 at^2 = 0.5* 1.5* 5^2 = 37.5 m
t = (100 - 37.5) / 15 = 4.167
tital time taken by car
T = 5 + t = 9.167 s
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
vx = 45 cos 19 = 42.55 m/s
vertical component of velocity
vy = 45 sin 19 - 9.8t =14.6 - 9.8 t
time taken by ball to reach home run
t = 115 /42.55 = 2.703 s
h = 1 + 14.6* 2.703 - 4.9* 2.703^2
h = 4.66 m
yes, the ball will clear the given height
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
Comment before rate in case any doubt, will reply for sure.. goodluck
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