Amanda S. answered • 10d
Current teach passionate about the hard sciences
To solve projectile motion questions, it is almost always useful to find the time first. The time is dependent on the vertical direction, because motion in the horizontal direction is constant. So, we first need to find how long it will take to fall the 3 m to the first shelf. We use the equation Δy=v_o*t + 1/2at^2. If the kick is horizontal, the initial velocity in the y direction is zero, which means we now have Δy= 1/2at^2. We know the rock is dropping with an acceleration down. If we assume down as the positive direction and plug in 3 for Δy 9.8 for a, we can solve for time. You can also assume down is the negative direction and plug in -3 and -9.8. As long as you’re consistent with your directions, you’re good. This gives us a time of 0.78. We know the rock will fall to
the shelf level in this time. In this same time, the rock needs to clear a horizontal displacement of 6m. The velocity in the horizontal direction is constant, so we can find the velocity by dividing the displacement by time. 6/0.78 is 7.67 and thus the velocity is 7.67 m/s forward.
We can use the total vertical drop to find the time of the entire flight in the same manner as before. Using 10 as Δy and 9.8 as a in the equation above, we get a time of 1.43. We now know the velocity in the horizontal direction is 7.67 and constant, so the velocity multiplied by time will give us the total horizontal range. The total range would this be 10.95 m. 6 of those meters are covered by the first shelf, so the remainder will be the distance from the second cliff. 10.95-6= 4.95. Thus, the rock will land 4.95 m from the bottom of the second cliff
