Answer :
Answer:
h = 56.57 ft
Explanation:
given,
angle at which tennis ball was hit = 26°
time taken to hit the cliff = 3.2 s
horizontal distance = 200 ft.
calculation of velocity
horizontal velocity,v_x = v cos θ
distance = speed x time
200 = v cos 26° x 3.2
v = 69.54 ft/s
now, calculation of time to reach maximum height
final velocity = 0 ft/s
vertical velocity = v sin θ
using equation of motion
v = u + at
0 = v sin 29° - g t
32.2 t = 69.54 sin 29°
t = 1.053 s
vertical distance of maximum height travel by the ball
[tex]s = u t +\dfrac{1}{2}gt^2[/tex]
[tex]x= 69.54\times sin 29^0\times 1.053-\dfrac{1}{2}\times 32.2\times 1.053^2[/tex]
x = 17.64 ft
now,
height of the cliff
distance traveled by the ball from top point to ground= x + h
time taken = t' = 3.2 - 1.053 = 2.147 s
initial velocity = 0 ft/s
using equation of motion
[tex]s = u t +\dfrac{1}{2}gt^2[/tex]
[tex]x + h =0 +\dfrac{1}{2}\times 32.2\times 2.147^2[/tex]
[tex]17.64 + h =74.21[/tex]
h = 56.57 ft
height of the cliff is equal to 56.57 ft