Question

The acceleration due to gravity at the surface of Mars is roughly 2/5 of Earth’s “g”. If an astronaut on Mars were to toss a wrench upward with a speed of 10 m/s, find a) how long it would rise, b) how high it would go, c) its speed at t = 3.0s , and d) its displacement at t = 3.0s.

Answer 1

Using the kinematic formula (see https://www.khanacademy.org/science/physics/one-dimensional-motion/kinematic-formulas/a/what-are-the-kinematic-formulas), obtain the following.

a) Time of rise as the time required to come to zero velocity at the highest point:

$$t = \dfrac{v_0}{g}$$

where $v_0 = 10m/s,g = \dfrac25\cdot9.8m/s^2 =3.92m/s^2$. Thus, obtain:

$$t = \dfrac{10^2}{3.92} \approx 26s$$

b) Distance, travelled by this time, which is the maximum height:

$$h = \dfrac{v_0t}{2} = \dfrac{10\cdot 26}{2} = 130m$$

c) Speed at t=3s:

$$v = |v_0-gt|= |10m/s - 3.92m/s^2\cdot 3s|\approx 1.8m/s$$

d) Displacement at t=3s:

$$d = v_0t-\dfrac{at^2}{2} = 10m/s\cdot 3s - \dfrac{3.92m/s^2\cdot (3s)^2}{2}\approx 12m$$