Question

Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground below with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is about 33.3 m/s. Bob starts the stopwatch as he throws the ball (with no way to measure the ball\'s initial trajectory), and watches carefully. The ball rises and then falls, and after 0.910 seconds the ball is once again level with Bob. Bob can\'t see well enough to time when the ball hits the ground. Bob\'s friend then measures that the ball landed 122 m from the base of the cliff. How high up is Bob, if the ball started from exactly 2 m above the edge of the cliff?

Answer 1

81 mph

81 * 5280 = 427,680 ft/hr / (60 s/min * 60 min/hr===> 3600 s/hr) = 118.8 ft/s

time up = time down ===> time up = 0.51 s / 2 = 0.255 s

vy = at = 32.17 ft/s^2 * 0.255 s = 8.20 ft/s Vertical component of velocity

So we know the hypotenuse and the opposite side===> We can find the Launch Angle

Sin^-1 a = 8.2 / 118.8 =

a = 3.96 degrees ===> Now we can find the horizontal component of velocity

cos 3.96 = x/118.8

vx = 118.52 ft/s

How high did the ball go?

d = 0.5at^2
d = 0.5 * 32.17 ft/s^2 * 0.255^2
d = 1.05 ft The ball fell from there under gravity

How long to go 398 ft at 118.52 ft/s

t = d/vx = 398/118.52 = 3.36 s

Subtract the time up to get the time to fall

3.36 s - 0.255 s = 3.10 s to fall from maximum height

d = 0.5at^2
d = 0.5 * 32.17 ft/s * 3.10^2
d = 154.88 ft

Subtract the height from Bob's hand to the max height

154.88 - 1.05 = 153.83 ft

Subtract Bob's height

153.83 - 5 = 148.83 ft height of the cliff

similar one but with different numericals hope u give me points for helping though . sorry for the inconvenience just plugin numbers and any doubts ping me

Question for the above answer is

Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use is a baseball, stopwatch, and a friend on the ground below with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is 81.0mph. Bob starts the stopwatch as he throws the ball (with no way to measure the ball's initial trajectory) and watches carefully. The ball rises and then falls, and after 0.510 seconds the ball is once again level with Bob. Bob can't see well enough to time when the ball hits the ground.Bob's friend then measures that the ball landed 398 ft. from the base of the cliff. How high up is Bob, if the ball started from exactly 5ft above the edge of the cliff?

_______ ft