Map Sapling Learning macmillan learning b has just finished climbing a sheer cli

Question

Map Sapling Learning macmillan learning b has just finished climbing a sheer cliff above a level beach, and wants to figure out how high he climbed. All he has to use 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 34.1 m/s Bob starts the stopwatch as he throws the ball (with no way to measure the ball's initial traiectory), and watches carefully. The ball rises and then falls, and after 0.710 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 hit the ground 122 m from the base of the cliff. How high above the beach was the ball when it was thrown Number 62 34.1 m/s 0.710 s There is a hint available! View the hint by clicking on the bottom divider bar. Click on the divider bar again to hide the hint. Close 122 m

Explanation / Answer

Here ,

let the angle made by the ball's velocity with horizontal is theta initially

time of flight = 2 * 34.1 * sin(theta)/9.8

0.710 = 2 * 34.1 * sin(theta)/9.8

theta = 5.9 degree

Now, for the initial height , h

Using equation of trajectory of projectile

y = y0 + x * tan(theta) - 0.50 * g * x^2/(u * cos*theta)^2

0 = h + 122 * tan(5.9 degree) - 0.50 * 9.8 * 122^2/(34.1 * cos(5.9 degree))^2

solving for h

h = 50.8 m

the height of the cliff is 50.8 m

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