Question

# The velocity v , in meters per second, of a falling object on Earth after t seconds, ignoring the effect of air resistance, is modeled by the equation v = 9.8t . There is a different linear relationship between time and velocity on Mars, as shown in the table below.

If an object dropped toward the surface of Earth has a velocity of 58.8 meters per second after t seconds, what would be the velocity of the same object dropped toward the surface of Mars after t seconds, ignoring the effect of air resistance?

- 15.9 meters per second
meters per second
- 22.2 meters per second
- 36.2meters per second
- 88.8 meters per second

Hint:

**Hint:**

First, we find the modelled equation of velocity of falling object on mars from the data in the table given. Then we find the time from the equation of velocity of falling object on Earth with the help of given condition in the question and use it in the equation of velocity of object on Mars to find the velocity.

## The correct answer is: 22.2 meters per second

### First we find the equation of velocity of a falling object on Mars (ignoring the effect of air resistance).

It is given that the relationship is linear, so the ratio of velocity and time is constant.

From the table, we have

Thus, the equation of velocity with respect to time of a falling object on Mars is v = 3.7t

Given, equation of velocity of a falling object on Earth with respect to time is v = 9.8t

According to the question, an object dropped toward the surface of Earth has a velocity of 58.8 meters per second after *t *seconds

By the equation v = 9.8t , the time after which the velocity is 58.8 metres per second is given by

We need to find the velocity of the same object dropped towards the surface of mass after t=6 seconds

By the relation v = 3.7t , we get the velocity to be

Thus, the correct option is B)

**Note:**

When we get time t = 6 seconds, we can find the answer directly from the options. As 6 is between 4 and 8, and the relation is linear,

so the velocity is between 14.8 metres per second and 29.6 metres per second.

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