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 Valkarth Mar 29th 2018 10:24 PM

Projectile Motion - Hitting a Sloped Wall

Question:
In the figure, a ball is launched with a velocity of magnitude 7.00 m/s, at an angle of 43.0° to the horizontal. The launch point is at the base of a ramp of horizontal length d1 = 6.00 m and height d2 = 3.60 m. A plateau is located at the top of the ramp. (a) Does the ball land on the ramp or the plateau? When it lands, what are the (b) magnitude and (c) angle of its displacement from the launch point?

The ball does in fact land on the ramp; not making it to the plateau. However, I don't know how to find the x and y distances of the impact. I have a feeling that I need to use the [x = Velocity * cos(theta)*time] equation and plug it into my [y=y0 + ut + 1/2gt^2] equation to solve for time, but i'm just not getting the right answer.

Any suggestions?

 Woody Mar 30th 2018 05:13 AM

Your equation [y=y0 + ut + 1/2gt^2] is correct but...

Note that [u] in the above equation is the initial vertical component of the velocity and (y0 is zero).
let us call the vertical component of velocity uy
so [uy=7.0*sin(43.0°)]

Also the ramp is rising according to the equation [y=d2/d1*x]
where x is the horizontal distance moved by the ball.

x will depend on the horizontal velocity of the ball
let us call it ux
so [ux=7.0*cos(43.0°)]
Now we can see that: [x=ux*t]

this gives us 2 equations for y:
[y=d2/d1*7.0*cos(43.0°)*t]
and:
[y=7.0*sin(43.0°)t + 1/2gt^2]

At what t (other than zero) do these two equations give the same answer?
What is x at this time?
is this less than 6m?

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