Question

If an arrow is shot upward on the moon with a velocity of 58 m/s, its height (in meters) after t seconds is given by H = 58t − 0.83t2. (a) Find the velocity of the arrow after two seconds. m/s (b) Find the velocity of the arrow when t = a. m/s (c) When will the arrow hit the surface? (Round your answer to one decimal place.) t = s (d) With what velocity will the arrow hit the surface? m/s

Answer 1

a) v = 54.7m/s

b) v = (58 - 1.66a) m/s

c) t = 69.9 s

d) v = -58.0 m/s

Step-by-step explanation:

Given;

The height equation of the arrow;

H = 58t - 0.83t^2

(a) Find the velocity of the arrow after two seconds. m/s;

The velocity of the arrow v can be given as dH/dt, the change in height per unit time.

v = dH/dt = 58 - 2(0.83t) ......1

At t = 2 seconds

v = dH/dt = 58 - 2(0.83×2)

v = 54.7m/s

(b) Find the velocity of the arrow when t = a. m/s

Substituting t = a into equation 1

v = 58 - 2(0.83×a)

v = (58 - 1.66a) m/s

(c) When will the arrow hit the surface? (Round your answer to one decimal place.) t = s

the time when H = 0

Substituting H = 0, we have;

H = 58t - 0.83t^2 = 0

0.83t^2 = 58t

0.83t = 58

t = 58/0.83

t = 69.9 s

(d) With what velocity will the arrow hit the surface? m/s

from equation 1;

v = dH/dt = 58 - 2(0.83t)

Substituting t = 69.9s

v = 58 - 2(0.83×69.9)

v = -58.0 m/s