Math Problem Statement

If a rock is thrown upward on the planet Mars with a velocity, find the following: (a) velocity after 2 seconds, (b) velocity at time t = a, (c) time when the rock will hit the surface, (d) velocity with which the rock hits the surface.

Solution

The image you uploaded shows a physics problem related to a rock being thrown upward on Mars. To help solve the problem, I would need the initial velocity of the rock, which isn't visible in the screenshot. I will outline the steps to solve each part based on the typical physics equations for projectile motion.

Assuming the acceleration due to gravity on Mars is g=3.71m/s2g = 3.71 \, \text{m/s}^2 (which is approximately true), here’s how we can approach the questions:

(a) Find the velocity after 2 seconds

The velocity of the rock at any time tt can be found using the equation: v(t)=v0gtv(t) = v_0 - g \cdot t where:

  • v0v_0 is the initial velocity (unknown from the image, but necessary),
  • gg is the acceleration due to gravity on Mars (g=3.71m/s2g = 3.71 \, \text{m/s}^2),
  • t=2t = 2 seconds.

(b) Find the velocity at time t=at = a

This is a general form of the same equation for velocity: v(a)=v0gav(a) = v_0 - g \cdot a where aa is a variable time. You would need to plug in the value of aa when given.

(c) When will the rock hit the surface?

The rock will hit the surface when its displacement s=0s = 0 (assuming it returns to the same height from

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Math Problem Analysis

Mathematical Concepts

Projectile Motion
Kinematics
Physics of Gravity

Formulas

v(t) = v_0 - g * t
s(t) = v_0 * t - 0.5 * g * t^2
v^2 = v_0^2 - 2 * g * h

Theorems

Kinematic Equations
Newton's Laws of Motion

Suitable Grade Level

Grades 9-12