Question

A rocket is launched with a velocity of 30 m/s at 40° to the horizontal. How far will it

travel horizontally?

Answer 1

The rocket will travel approximately 162 meters horizontally.

Step-by-step explanation:

To find the horizontal distance traveled by the rocket, we need to consider the horizontal component of its initial velocity. This can be found using the equation:

horizontal velocity = initial velocity * cos(angle)

Given that the initial velocity is 30 m/s and the angle is 40°, we can calculate:

horizontal velocity = 30 m/s * cos(40°) ≈ 23 m/s

Now, we can find the time the rocket will be in the air using the equation:

time = horizontal distance / horizontal velocity

Assuming the rocket lands at the same height it was launched, the vertical distance traveled is 0. Therefore, the horizontal distance is equal to the range of the rocket. Using the formula for the range of a projectile with initial velocity v and launch angle θ:

range = (v^2 * sin(2θ))/g

where g is the acceleration due to gravity (approximately 9.8 m/s²).

Plugging in the values, we get:

range = (30 m/s)^2 * sin(2 * 40°) / 9.8 m/s² ≈ 162 meters

Answer 2

A. Rocket A will travel farther horizontally than rocket B.

Step-by-step explanation:

This is because from the x axis, 40 m/s at 90 degrees travels directly vertical. 40 m/s at 70 degrees is slightly horizontal, so it will travel further horizontally.