Respuesta :
Answer:
[tex]d_1 = 16 d[/tex]
Explanation:
As we know that initial speed of the fall of the stone is ZERO
[tex]v_i = 0[/tex]
also the acceleration due to gravity on Mars is g
so we have
[tex]d = v_i t + \frac{1}{2}gt^2[/tex]
now we have
[tex]d = 0 + \frac{1}{2}g t^2[/tex]
now if the same is dropped for 4t seconds of time
then again we will use above equation
[tex]d_1 = 0 + \frac{1}{2}g(4t)^2[/tex]
[tex]d_1 = 16(\frac{1}{2}gt^2)[/tex]
[tex]d_1 = 16 d[/tex]
The distance covered by the rock during the [tex]4t[/tex] seconds of its fall will be [tex]\fbox{16d}[/tex].
Explanation:
Given:
Distance covered by the rock in [tex]t\text{ sec}[/tex] is [tex]d[/tex].
Concept:
As the astronaut drops the rock from the top of a cliff, the stone falls freely under the acceleration due to gravity of the Mars. This motion of the rock on the surface of the mass occurs according to the second equation of motion.
[tex]\boxed{S=v_it+\dfrac{1}{2}g_mt^2}[/tex]
Here, [tex]S[/tex] is the distance covered by the rock, [tex]v_i[/tex] is the initial velocity of the rock, [tex]g_m[/tex] is the acceleration due to gravity on the surface of Mars and [tex]t[/tex] is the time for which the rock falls.
Since the rock is dropped from the top of the cliff, the rock will not have any initial velocity. So, the initial velocity of the rock will be zero.
Substitute the values in the given equation.
[tex]d=0(t)+\dfrac{1}{2}g_mt^2\\d=\dfrac{1}{2}g_mt^2[/tex]
Now, in order to find the distance covered by the rock as it falls for time [tex]4t[/tex], substitute [tex]4t[/tex] for [tex]t[/tex] in the above expression.
[tex]\begin{aligned}d'&=0(t)+\dfrac{1}{2}g_m(4t)^2\\&=16.\dfrac{1}{2}g_mt^2\end{aligned}[/tex]
Substitute [tex]d[/tex] for [tex]\dfrac{1}{2}g_mt^2[/tex] in above expression.
[tex]d'=16.d[/tex]
Thus, The distance covered by the rock during the [tex]4t[/tex] seconds of its fall will be [tex]\fbox{16d}[/tex].
Learn More:
1. Effect on the acceleration while sliding down the hill https://brainly.com/question/2286502
2. Expression for the acceleratuon of the block under friction https://brainly.com/question/6088121
3. Magnitude of acceleration of the car https://brainly.com/question/6423792
Answer Details:
Grade: High School
Subject: Physics
Chapter: Acceleration
Keywords:
Mars, cliff, stone, acceleration, gravity, falls, rock, top, time, t, 4t, distance, ground, equation of motion, initial velocity.
