Solving Projectile Motion Problem: 4.2 m/s

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Jim needs to roll a ball off a diving board 10 m high to hit his friend Bob, who is 6 m away horizontally. The time it takes for the ball to fall is calculated using the equation s = ut + 1/2at², leading to a time of approximately 1.1 seconds. However, the correct speed to roll the ball is 4.20 m/s, not the 5.45 m/s calculated. The error arises from misunderstanding the relationship between horizontal and vertical motion, as they are independent. The calculations must correctly account for both components to determine the accurate speed needed.
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Homework Statement


Jim stands with a ball at the rear of a diving board, 10 m above the
surface of a swimming pool. His friend Bob is swimming below, at a
horizontal distance of 6 m from the front of the board. Jim thinks it
would be funny to roll his ball along the diving board so that it drops on
Bob’s head. Assuming that the effects of friction and air resistance are
negligible, calculate the speed (in m s-1) at which Jim must roll the
ball.

Homework Equations


s=u+1/2at^2
speed=distance/time

The Attempt at a Solution


rearranged s=u+1/2at^2 to find t
t=1.1s
speed 6/1.1=5.45m/s
However the answer is 4.20m/s
where did I go wrong?
 
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fleur said:

Homework Statement


Jim stands with a ball at the rear of a diving board, 10 m above the
surface of a swimming pool. His friend Bob is swimming below, at a
horizontal distance of 6 m from the front of the board. Jim thinks it
would be funny to roll his ball along the diving board so that it drops on
Bob’s head. Assuming that the effects of friction and air resistance are
negligible, calculate the speed (in m s-1) at which Jim must roll the
ball.

Homework Equations


s=u+1/2at^2
speed=distance/time

The Attempt at a Solution


rearranged s=u+1/2at^2 to find t
t=1.1s
speed 6/1.1=5.45m/s
However the answer is 4.20m/s
where did I go wrong?
Why don't you show us your calculations of how you obtained t = 1.1 s for the time it takes the ball to fall from the board and hit the water.
 
SteamKing said:
Why don't you show us your calculations of how you obtained t = 1.1 s for the time it takes the ball to fall from the board and hit the water.
I did square root of 2x6/9.81
 
fleur said:
I did square root of 2x6/9.81
So the ball is falling horizontally? I thought the board was 10 m above the surface of the water.
 
The equation is wrong

fleur said:

Homework Equations


s=u+1/2at^2
The equation is s=ut+1/2at2

fleur said:
I did square root of 2x6/9.81

The time taken for it to hit the pool when dropped is the same as when rolled since the horizontal and vertical components of the velocity do not affect each other.
 
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