Problem in section 27 page 151 of the book problem 14 If a r

Problem in section 2.7 page 151 of the book problem 14. If a rock is thrown upward on the planet Mars with a velocity of 10m/s, its height(in meterers) after t seconds is given by H=10t-1.86t^2. a) find the velocity fo the rock after one second. b) Find the velocity of the rock when t=a. c) When will the rock hit the surface? d) With what velocity will the rock hit the surface?

Solution

given height = 10t-1.86t^2
height = ut - 0.5a t^2
comparing with above equation
u = 10 = initial velocity
0.5a = 1.86
=> a = 3.72
where a is the acceleration, downwards
velocity = initial - acceleration*time
= 10 -3.72*1
= 6.28
Velocity at time t = a
velocity = initial - acceleration*time
velocity = 10 - 3.72*a

rock will hit the ground after time = 2*initial velocity/ acceleration
= 2*10/3.72
= 5.376 seconds

rock will hit the ground with initial velocity = 10 m/s