   Chapter 3, Problem 37AP

Chapter
Section
Textbook Problem

A father demonstrates projectile motion to his children by placing a pea on his fork’s handle and rapidly depressing the curved tines, launching the pea to heights above the dining room table. Suppose the pea is launched at 8.25 m/s at an angle of 75.0° above the table. With what speed does the pea strike the ceiling 2.00 in above the table?

To determine
The speed with which the pea strikes the ceiling.

Explanation

The horizontal component of the velocity is,

vx=v0cosθ

Here,

v0 is the initial velocity

θ is the angle of projection

Substitute 8.25m/s for v0 and 75.0° for θ .

vx=(8.25m/s)cos75.0°=2.14m/s

In the vertical direction,

vy2=v0y22gΔy=v02sin2θ2gΔy

Here,

vy is the vertical velocity

v0y is the vertical component of the initial velocity

g is the acceleration due to gravity

Δy is the vertical displacement

θ is the angle of projection

Substitute 8.25m/s for v0 , 75.0° for θ , 9.80m/s2 for g and 2m for Δy

vy2=(8

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