   Chapter 12.3, Problem 27E

Chapter
Section
Textbook Problem

# Projectile Motion In Exercises 27-40, use the model for projectile motion, assuming there is no air resistance and g = 32 feet per second per second.A baseball, hit 3 feet above the ground, leaves the bat at an angle of 45 ∘ and is caught by an outfielder 3 feet above the ground and 300 feet front home plate. What is the initial speed of the ball, and how high does it rise?

To determine
The initial speed of the baseball and maximum height of the ball.

Explanation

Given:

A baseball, hit 3ft above the ground leaves the bat at an angle of θ=45° and catch by the fielder 300ft from home plate.

Explanation:

The position vector as shown below,

r(t)=(v0cosθ)t.i^+[h+(v0sinθ)t12t2]j^      =v02t.i^+[3+v02t16t2] v02t=300 when, 3+v02t16t2=3so t=3002v0  and v02(3002v0)16(3002v0)=0                        3003002

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