1. Two balls are shot with the same initial velocity - one is shot horizontally

Question

1. Two balls are shot with the same initial velocity - one is shot horizontally and the other is shot at an angle of 10 degrees above the horizontal. Which ball goes further? Explain your reasoning.

2. For a ball shot horizontally with a speed of v0 from a height of y0, what is the expression for the horizontal displacement of the ball in terms of v0, y0, and g (no time!)?

3. Use your expression from the previous question to find the horizontal displacement of a ball with an initial speed of 5 m/s and an initial height of 1.75 m being shot horizontally.

Explanation / Answer

Ball shot horizontally will cover more distance because when ball thrown at 10 angle above a horizontal then horizontal component of velocity will be u cos 10 and it will be than u

Horizontal distance = vo x t = vo x (2yo/g)^1/2

above eq can be derive using eq of motion in two dimension

X= Uxt+1/2ax t^2(where ux and ax are component of velocity and acceleration in x direction )

Because ax =0

So x = vot....... eq. 1

y =uyt + 1/2 ay t ^2.

yo= 1/2 g t^2

t=( 2yo/g)^1/2 substitute value of t in eq 1 we get

x =vo( 2yo/g)^1/2

X =5 ( 2 x1.75/9.8)^1/2 =2.988m

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