Physics question

Question

If a marble is launched straight upward at a speed of 15 m/s and doesn't hit anything on its way up or down, it will reach a height of about 11.5 m above the launch point before it starts falling back down, and exactly 2.0 s after launch, it will be 10.4 m above the launch point and moving downward at a speed of 4.6 m/s. Calculate the (a) distance traveled, (b) displacement,

(c) average speed, and (d) average velocity of the marble during the 2.0 s after launch.

Answer 1

Given data:

Initial velocity (u) = 15 m/s (upward)

Time (t) = 2.0 seconds

Height above the launch point at t = 2.0 seconds = 10.4 m

(a) To calculate the distance traveled during the 2.0 seconds after launch, we can use the formula for displacement:

s = ut + 1/2at^2

Where:

s is the displacement (distance traveled)

u is the initial velocity

t is the time

a is the acceleration due to gravity (approximately -9.81 m/s², considering the downward direction)

s = (15m/s)*(2.0s) + 1/2*(-9.81m/s^2)(2.0s)^2

s = 30m - 19.62m = 10.38m

So, the distance traveled by the marble during the 2.0 seconds after launch is approximately 10.38 meters

(b) The displacement is the change in position from the initial point to the final point. Since the marble returns to its starting point, the displacement is zero.

(c) To calculate average speed, you can use the formula:

Average speed = Total distance / Total time

In this case, the total distance is the same as the distance traveled, which is 10.38 meters, and the total time is 2.0 seconds.

Average speed = 10.38m / 2.0s = 5.19m/s

So, the average speed of the marble during the 2.0 seconds after launch is 5.19 m/s.

(d) To calculate average velocity, you can use the formula:

Average Velocity = Total displacement / Total time

In this case, the total displacement is zero (as explained in part b), and the total time is 2.0 seconds.

Average Velocity = 0m / 2.0s = 0 m/s

So, the average velocity of the marble during the 2.0 seconds after launch is 0 m/s. This makes sense because the marble returns to its starting point, so its overall displacement is zero. Hopefully, this helps