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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The height (in meters) of a projectile shot vertically upward from a point 2m above ground level with an initial velocity of 24.5 m/s is h = 2 + 24.5t – 4.9t2 after t seconds.

(a) Find the velocity after 2 sand after 4 s.

(b) When does the projectile reach its maximum height?

(c) What is the maximum height?

(d) When does it hit the ground?

(e) With what velocity does it hit the ground?

(a)

To determine

To find: The velocity after 2 s and after 4 s if the height of the projectile shot vertically upward from 2 m above the ground level is h(t)=2+24.5t4.9t2 with an initial velocity of 24.5 m/s.

Explanation

The height of the particle is, h(t)=2+24.5t4.9t2.

Find the derivative of h(t) and obtain the velocity.

v(t)=h'(t)=24.59.8t

Thus, the velocity is v(t)=24.59.8t (1)

Substitute t  = 2 in equation (1) and obtain the velocity after 2 s

(b)

To determine

To find: when the projectile reach its maximum if the height of the projectile shot vertically upward from 2 m above the ground level is h(t)=2+24.5t4.9t2 with an initial velocity of 24.5 m/s.

(c)

To determine

To find: when the projectile reach its maximum if the height of the projectile shot vertically upward from 2 m above the ground level is h(t)=2+24.5t4.9t2 with an initial velocity of 24.5 m/s.

(d)

To determine

To find: When the projectile hits the ground if the height of the projectile shot vertically upward  from 2 m above the ground level is h(t)=2+24.5t4.9t2 with an initial velocity of 24.5 m/s.

(e)

To determine

To find: With what velocity the projectile hits the ground if the height of the projectile shot vertically upward from 2 m above the ground level is h(t)=2+24.5t4.9t2 with an initial velocity of 24.5 m/s.

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