Gradebook uestion 11 of 12 3 Sapling Learning a Bob has just finished climbing a

Question

Gradebook uestion 11 of 12 3 Sapling Learning a 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 71.0 mph. 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 fails, and after 0.910 seconds the ball is once again level with Bob. Bob can't see well e the ba to time when the ball hits the ground. Bob's friend then measures that the ball edge of the clif? ft 71.0 mph 5 ft 332 ft

Explanation / Answer

71 mph

71 * 5280 = 374,880 ft/hr / (60 s/min * 60 min/hr===> 3600 s/hr) = 104.13 ft/s

time up = time down ===> time up = 0.91 s / 2 = 0.455 s

vy = at = 32.17 ft/s^2 * 0.455 s = 14.64 ft/s Vertical component of velocity

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

th = Sin^-1(14.64 / 104.13 )

th = 8.08 degrees ===> Now we can find the horizontal component of velocity

cos 8.08 = vx/104.13

vx = 103.1 ft/s

How high did the ball go?

d = 0.5at^2

d = 0.5 * 32.17 ft/s^2 * 0.455^2

d = 3.33 ft The ball fell from there under gravity

How long to go 332 ft at 103.1 ft/s

t = d/vx = 332/103.1 = 3.22 s

Subtract the time up to get the time to fall

3.22 s - 0.455 s = 2.77 s to fall from maximum height

d = 0.5at^2

d = 0.5 * 32.17 ft/s * 2.77^2

d = 122.99 ft

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

122.99 – 3.33 = 119.66 ft

Subtract Bob's height

119.66 - 5 = 114.66 ft height of the cliff

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