Finding the Distance for a Projectile to Land on a Moving Cart

[judas_priest]

Homework Statement

A ball is kicked horizontally with speed v1 from the top of a building of height h. A small cart is moving towards the building with a constant speed v2. Right at the instant when the ball is kicked, the cart is at a distance d from the building. What is the distance d so that the ball lands right on top of the cart? You can neglect the dimensions of the cart with respect to the height of the building h. Express your answer in terms of some or all of the variables h, v1, v2 and g

Homework Equations

The Attempt at a Solution

I tried to equate the time taken (since they meet at the same time). I made sure to include 'd' in my equation, because that's the variable needed to be found

Here's my equation.

x/v1 = d-x/v2.

Where x is the distance traveled by the ball in x direction and d-x is the distance traveled by the cart.

The questions needs an 'h' in the answer. I can't get the term in my answer

 

[STEMucator]

Hmm, the way I see this problem is you first need to find the total horizontal displacement of the ball ( I posted how to do so in your other thread ).

With this in mind, you know exactly how far away the cart will need to be from the building for the ball to land inside of it.

 

[judas_priest]

I too did it that way. But the answer needs a 'h'. Like the question says.

 

[STEMucator]

I too did it that way. But the answer needs a 'h'. Like the question says.

Express your answer in terms of some or all of the variables h, v1, v2 and g

I don't see how the height of the building is relevant in this case. The height of the building would be used to calculate the total time the ball was in the air.

 

[voko]

x/v1 = d-x/v2.

This is one equation and two unknowns. You need another equation for a definite solution. Think how the height affects the motion.