Answer:
ax = 6.43m/s²
Explanation:
The acceleration is the time derivative of the velocity function ax = dvx(t)/dt
We have been given the velocity function v(t) and also the velocity v = 12.0m/s and we are requested to calculate the acceleration at this time which we don't know.
So the first step is to calculate the time at which the velocity =12.0m/s and with this time calculate the acceleration. Detailed solution can be found in the attachment below.
A) 2.64 H
The maximum height that the expelled rock can reach can be found by using the equation:
where
v = 0 is the velocity at the maximum height
u is the initial velocity
g is the acceleration of gravity
d is the maximum height
Solving for d,
We see that the maximum heigth is inversely proportional to g. On the Earth,
and
So we can write:
where H' is the maximum height reached on Mars, and is the acceleration of gravity on Mars. Solving for H',
B) 2.64T
The time after which the rock reaches the maximum height can be found by using
where
v = 0 is the velocity at the maximum height
u is the initial velocity
Solving for t,
The total time of the motion is twice this value, so:
So we see that it is inversely proportional to g.
On the Earth, t = T. So we can write:
where T' is the total time of the motion on Mars. Solving for T',