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fjdd The velocity of a projectile fired up into the air follows the equation sho

ID: 1329657 • Letter: F

Question

fjdd The velocity of a projectile fired up into the air follows the equation shown below: v(t) = 40 - 4 t m/s Determine the time when the projectile reaches its maximum height For the velocity in Problem #1, determine the values of time when the velocity is larger than 4 m/s. (i.e., v ( t ) > 4 ) For the velocity in Problem #1, determine the values of time when the magnitude of the velocity is less than or equal to 8 m/s. (i.e., v(t) Ge 8) For the velocity in Problem #1, determine the values of time when the magnitude of the velocity exceeds 12 m/s. (i.e., v (t) > 12)

Explanation / Answer

(1)

the given equation is

v (t) = 40 - 4 t

at t = 0 the initial velocity will be

u = v (0)

= 40 m / s

the maximum height attained will be

Hmax= u2/ 2 g

= (40 x 40) (2 x 9.8)

= 81.6 m

time taken to reach maximum height will be the time of ascent

ta = 40 / 9.8

= 4.08 s

(2)

if the velocity greater than 4 that is

v(t) > 4 say it is 5 m / s then

5 = 40 - 4 t

t = 35 / 4

= 8.75 s

(3)

when v(t) = 8.0 m / s

8.0 = 40 - 4 t

4 t = 40 - 8

t = 32 / 4

= 8 s   

(4)

if exceeds 12 m / s then let the velocity be 13.0 m / s then

13.0 = 40 - 4 t

t = 6.75 s