Find velocity, acceleration, height.

Question

A rock thrown vertically upward from the surface of the moon at a velocity of

4 m/sec reaches a height of s=4t−0.8t² meters in t sec.

a. Find the​ rock's velocity and acceleration at time t.

b. How long does it take the rock to reach its highest​ point?

c. How high does the rock​ go?

d. How long does it take the rock to reach half its maximum​ height?

e. How long is the rock​ aloft?

Answer 1

a. v=ds/dt = 4-1.6t m/s a=dv/dt =-1.6m/s²

b. rock reaches highest point when v=0 so 0=4-1.6t t=4/1.6 s = 2.5s

c s= 4(2.5) - .8(2.5)² =10 - 5 =5m

d. s=2.5= 4t -.8t² so .8t²-4t +2.5 =0 reduce by dividing by 4 to get .2t² -t

+ .625 =0 use the algebra formula to solve for t which gives the following:

t= (1 ±√(1- .8))/.4 t=1/.4± √.2/.4 t=2.5±.447/.4 t=2.5±1.118 s so since t

must be less than 2.5s from part b then t= 1.38s.

e. The rock is in the air for 5s when it hits the ground.