Projectile Motion (Regular Physics) question

[Jonathen]

Homework Statement

A ball was let go at the top of a ramp 15 cm. high and 70.5 cm long it then goes to drop off the end of a 92 cm. table after it leaves the ramp how far will the ball land from the table. This is for a general physics class so neglect air resistance and use 10.0 m/s^2 for gravity, I am not sure if you need to use angles we have not used them before and this was a actual lab in which we had to land the ball into a cup, we had to position the cup meaning we needed to know where the ball would land. Thank You.

Homework Equations

The Attempt at a Solution

 

[danago]

Calculate the speed of the ball at the end of the ramp and also the angle at which it is projected from the table. Calculate the vertical and horizontal components of the initial velocity, and then use these to find the time that the ball is in the air for and therefore the distance it travels horizontally.

 

[Jonathen]

Will the angle of the ramp effect how fast it is going at the end of the ramp? if not will Vf=Vo+a(t) work? if it does how would I calculate the angle at which the ball is launched OFF OF THE TABLE? Thank you for replying so quickly.

 

[danago]

You can find the angle at which it is launched off the table by using trigonometry to find the rightmost angle in the ramp. Ill call this angle $$\theta$$.

The horizontal component of the velocity will be $$u_x=u\:cos(\theta)$$ and the vertical component will be $$u_y = u\:sin(\theta)$$ downwards. Given that you know the height of the ramp from the floor, you can use the vertical velocity to find the time before it hits the floor. You can then use this time with $$u_x$$ to find how far horizontally it travels.