Assume no air friction and that the acceleration due to gravity is 10 meters/sec^2. A ball is moving horizontally at a rate of 5 meters/sec. until it falls off the edge of a platform. The height, h, of the platform would have to be ___ meters if the ball hit the ground 8 meters from the foot of the platform.

I don't know how to start. You don't necessarily have to do the whole problem. I just need ideas on how to go about doing the problem! Thanks

the horizontal speed does not change. So, to hit 8m out, it would need to fall for

8m / 5m/s = 1.6 s

So, how far does it fall in 1.6 seconds?

To determine the height of the platform, we can use the kinematic equation of motion for vertical motion:

h = (1/2)gt^2

where:
h is the height of the platform,
g is the acceleration due to gravity (10 m/s^2 in this case),
and t is the time it takes for the ball to reach the ground.

First, we need to find the time it takes for the ball to hit the ground. Since there is no air friction, the horizontal velocity of the ball remains unchanged as it falls. This means that the time it takes for the ball to hit the ground is the same as the time it would take for the ball to cover a horizontal distance of 8 meters.

To find the time, we can use the formula for horizontal motion:

d = vt

where:
d is the distance (8 meters in this case),
v is the horizontal velocity of the ball (5 m/s in this case),
and t is the time.

Rearranging the formula, we get:

t = d/v

Substituting the given values, we find:

t = 8 m / 5 m/s = 1.6 s

Now that we have the time, we can substitute it into the kinematic equation to solve for the height of the platform:

h = (1/2)gt^2

h = (1/2)(10 m/s^2)(1.6 s)^2

Simplifying the equation, we find:

h = 12.8 meters

Therefore, the height of the platform would have to be 12.8 meters for the ball to hit the ground 8 meters from the foot of the platform.