Question

You are standing on a slope of 20 degrees to the horizontal and are going to throw a ball at vi=20 m/s up the incline. If you throw the ball at an angle of 45 degrees with respect to the horizontal at what distance up the incline from your feet does it land? Assume the ball leaves your hand directly overhead, h=2.0 m above the slope.

I know the horizontal velocity = 14.14 m/s and the vertical velocity also = 14.14 m/s. I calculated time to be 1.44 s half way and the full trip 2.88 s ( (vf-vi)/a = (0-14.14)/-9.8 = 1.44) . How does it being on an incline of 20 degrees affect the distance it is going to land from your feet?

Answer 1

Angle of projection of the ball with respect to surface of the slope is .

Considering it as the angle of projection this problem will become simple projectile motion with respect to slope with some initial height. Then distance up the incline where ball lands from your feet will be simply the range of ball when it touches the surface.

Now lets first calaculate Maximum Height,

Initial speed of projectile with relative angle of projection with respect to slope,

   ( parallel to slope up the incline)

Initial Vertical speed of projectile with respect to slope,

     

Considering vertical motion(with respect to slope) only, we know that at peak, projectile comes to rest momentarily, thus at maximum height final velocity of projectile will be

Acceleration acting vertically with respect to the slope,

( negative sign is used since gravity opposes the vertical motion)

Let Maximum height from point of throwing be h' , then by using equations of motion,

  

  ( from initial point of firing of projectile with respect to slope)

then Total maximum height from slope is H= (2+10.659)m= 12.659m

Let time taken to reach that maximum height(h') be t', then again using equations of motion,

  

Now considering 2nd part of its trip, when the projectile is at a height H= 12.659m

for this initial vertical velocity is u'= 0 m/s

vertical acceleration with respect to slope will be

( it will be positive as this time it will support this motion since it is the downward motion)

Let time taken by projectile to reach ground from this much is t, then by equations of motion,

  

Then total time taken for the motion is   

Then for horizontal distance travelled in this much time(Range of the ball when it hits the slope) is

acceleration in horizontal direction,

(Negative sign is used sign the horizontal motion of acceleration due to gravity will act down the slope thus for the motion up the slope it will act as the decceleration)

Then   

Using all given and deduced values in above,

  

  

As you can see that it iscoming out be negative which can't be possible thus it means that values you provided are somewhere wrong since method to solve this problem will be this only. Please crosscheck the values you provided and follow the above procedure. Then you'll get correct answer.