Question

A student is standing on a very steep hill, kicks a soccer ball horizontally with a speed of 10 m/s toward a student who is sitting on a level field 3 meters below. How long does it take the soccer ball to strike the ground?

Answer 1

Answer:

0.782 seconds

Explanation:

We are given that the ball starts out on a hill that is 3 m above a level field below. And that the ball is kicked horizontally. We are asked how long the ball takes to hit the ground 3 meters below.

On closer consideration of the given situation, it is important to realize that even though the ball starts out with a speed of 10m/s in the horizontal direction, that this will not make a difference in how fast the ball travels in the vertical direction (which is what the question is basically asking for). Hence for this question, we can ignore the initial horizontal speed of the ball and realize that the initial vertical speed is 0 m/s.

Recall that one of the equations of motion can be expressed as:

s = ut + (1/2) at²       (refer to attached for reference)

where,

Applied in the vertical direction,

s = vertical distance travelled = 3 meters in this case

u = initial vertical velocity = 0 m/s in this case

a = acceleration due to gravity, g = 9.81 m/s²

t = time taken ( we are asked to find this)

simply substituting the known values above into the equation:

s = ut + (1/2) at²

3 = 0 + (1/2) (9.81)t²

3 = 4.905t²

t² = 3 / 4.905

t² = 0.61162

t = √0.61162

t = 0.782 seconds