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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Projectile MotionIn Exercises 41 and 42, use the model for projectile motion, assuming there is no air resistance and g = 9.8 meters per second per second.

A projectile is fired from ground level at an angle 8° with the horizontal. The projectile is to have a range of 50 meters. Find the minimum initial speed necessary.

To determine

To calculate: The minimum initial velocity required to cover the range of 50m and at an angle of 8°.

Explanation

Formula used:

The path followed by a projectile is

r(t)=(v0cosθ)ti+[(v0sinθ)t+12gt2]j

And 2cosθsinθ=sin2θ

Calculation:

The projectile follows the path

r(t)=(v0cosθ)ti+[(v0sinθ)t4.9t2]j

Here,

x=(v0cosθ)t=50 …...…... (1)

y=(v0sinθ)t16t2=0 …...... (2)

Solve the equation (2).

(v0sinθ)t4.9t2=0t((v0sinθ)4.9t)=0

One obtain, t=0 and t=v0sinθ4.9

Put t=v0sinθ4

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Chapter 12 Solutions

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