How to Calculate Time and Displacement for a Ballistic Cart Launch

[lulusmith]

Hi,
I've tried to figure this out but I just can't! Please help me understand how to work it out?

A ballistic cart is a wheeled cart that can launch a ball in a direction perpendicular to the way the cart moves and can then catch the ball again if it falls back down on the cart. Holding the cart stationary on a horizontal track, you confirm that the ball does indeed land in the cart after it is launched. Let’s say that the cart launches the ball with an initial velocity of 5.50 m/s up relative to the cart while the cart is rolling with a constant velocity of 7.00 m/s to the right. Using g = 10.0 m/s2, and neglecting air resistance, determine

(a) the time it takes the ball to return to the height from which it was launched.

(b) the magnitude of the displacement of the cart during this time.

Thank you!

 

[mitch_1211]

part (a) is simply the total time of flight, i.e find the time until max height and then double it for the full trajectory. Part (b) is just the range of the ball, for the cart the catch it, it needs to travel the same distance as the ball has

hope this helps

 

[lulusmith]

Can't believe I couldn't do it before, I think I was just over thinking it.
Thank you! :D

 

[mitch_1211]

Can't believe I couldn't do it before, I think I was just over thinking it.
Thank you! :D

no worries at all :)

 

[PJC01]

Hello, calculating time and displacement for a ballistic cart launch involves understanding the principles of projectile motion and using the equations of motion. Let's break it down into two parts:

(a) Time: The time it takes for the ball to return to its initial height can be calculated using the equation t = 2v/g, where t is time, v is initial velocity, and g is acceleration due to gravity. In this case, the initial velocity is 5.50 m/s and the acceleration due to gravity is 10.0 m/s^2. Plugging these values into the equation, we get t = 2(5.50)/10.0 = 1.10 seconds.

(b) Displacement: The magnitude of the displacement of the cart during this time can be calculated using the equation s = ut + (1/2)at^2, where s is displacement, u is initial velocity, a is acceleration, and t is time. In this case, the initial velocity is 7.00 m/s, the acceleration is 0 (since the cart is moving at a constant velocity), and the time is 1.10 seconds. Plugging these values into the equation, we get s = (7.00)(1.10) + (1/2)(0)(1.10)^2 = 7.70 meters.

I hope this helps you understand how to calculate time and displacement for a ballistic cart launch. If you have any further questions, please don't hesitate to ask. Keep exploring and learning!