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Fundamentals Of Physics
Found in: Page 91

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Short Answer

A ball is thrown horizontally from a height of 20mand hits the ground with a speed that is three times its initial speed. What is the initial speed?

The initial speed of a ball is7m/s.

See the step by step solution

Step by Step Solution

Step 1: Given data

1) The final speed of a ball is three times its initial speed.

2) Height above the ground is, h=20m.

Step 2: Understanding the concept of projectile motion

Using the equations of projectile motion, we can find the initial velocity of a ball.When the object is thrown in the horizontal direction, its vertical component of the velocity is zero. As it moves down, it gains speed. Using this information and the kinematic equations, we can calculate the initial speed.


v2=V02+2ay-y0 …(i)

Step 3: Calculate the initial speed

Let the initial velocity of a ball is Vm/s.

So, the horizontal velocity, of a ball is Vx=Vm/s.

The initial vertical velocity of the ball is zero.

When the ball strikes the ground, it will have horizontal as well as vertical velocity. Let us assume that its vertical velocity when the ball is about to hit the ground is Vym/s.

So, the final speed 3Vis the magnitude of the final velocity. Hence,

3V=Vx2+Vy23V2=V2+Vy2 Vy2=8V2

Now, use the kinematic equation for the final velocity in the vertical direction.

From equation (i), we can write that

Vy2=v02-2g(y-y0)8V2=02-2x×(9.8m/s)×(0m-20m) V=7.0m/s

Therefore, the initial velocity with which the ball was thrown is 7.0m/s.

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