Question

A marble is launched from the floor at a speed of 8.1 m/s at an angle of 31 degrees above the horizontal. How far away from the starting point will the marble land?

Answer 1

To solve for the distance the marble will travel when launched at an angle, we must use projectile motion equations to resolve the initial velocity into its components, calculate the time of flight, and then determine the horizontal distance traveled.

Step-by-step explanation:

The question is asking us to calculate the horizontal distance a marble will travel when it is launched from the floor at a certain angle and initial speed. This problem can be solved using the equations of projectile motion.

Steps to solve the projectile motion problem:

1. Resolve the initial velocity into horizontal (vx) and vertical (vy) components using the angle given.
2. Calculate the time (t) the marble is in the air using the vertical component of the velocity and the equation vy = uy + ayt, where ay is the acceleration due to gravity (-9.81 m/s2, negative because it's in the opposite direction to the initial vertical velocity).
3. Using the time calculated in step 2, determine the horizontal distance traveled using the horizontal velocity component and the equation s = vxt.

This series of calculations will provide the distance from the starting point where the marble will land, assuming that air resistance is negligible.