A ball is thrown horizontally from a building 17m tall with a speed of 9 m/s. How far from the base of the building does the ball hit the ground?
I've never worked on two-dimensional physics problems before, so this one really has me baffled. I feel as if I haven't been given enough information to solve it. Please help me out so I can actually do the rest of this homework myself. D=
If I treat x and y as if they were completely independent, I would just have a speed of 9 m/s going in the x direction. That doesn't give me anything to work with. In the case of y, there's only the height of the building and acceleration due to gravity. Would it be possible to solve for the velocity in the y direction with just 17m and g? If so, I am not so sure how.
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Verified answer
The horizontal and vertical velocities are completely independent - there is a convincing lab demonstration for this involving the release of 2 identical ball bearings (large) from the same height and at the same time .. one is projected horizontally, while the other just drops vertically. Both balls strike the floor at the same instant, indicating that a horizontal component made no difference to vertical motion. (I hope you get to see that kind of demonstration)
The independence assumes that air resistance has a negligible effect on the motion.
In these cases we assume that the initial horizontal velocity (9.0m/s) will be retained throughout the flight (air resistance negligible) .. and superimposed onto this is the normal free-fall vertical acceleration giving a progressively faster vertical component to the motion.
The distance from the base will be the horizontal velocity x time of flight.
Time of flight is obtained from the vertical free-fall that is happening at the same time ..
Vertically ..
• initial velocity, u = 0
• acceleration, a = 9.80m/s² (free-fall accel.due to gravity)
• distance, d = 17.0m (vertically)
Apply [ d = ut ½.at² ] to the vertical motion to get t
17.0 = (0) + ½ x 9.80 x t² ..
t² = 17.0 / 4.90 = 3.47 s
So, horizontal distance moved during the 3.47s flight = 9.0m/s x 3.47s .. .. ►d = 31.23 m