On the surface of the Moon, a ball is thrown horizontally, with a speed of 15 m/s, from the top of a 6 m tall hill. How far from the point on the ground directly below the launch point does the ball strike the ground? (On the Moon, the acceleration due to gravity is only 1.67 m/s2.)
To find the horizontal distance the ball travels before hitting the ground, we need to determine the time it takes for the ball to fall from the top of the hill to the ground. Here are the steps to solve the problem:
Step 1: Find the time it takes for the ball to fall from the top of the hill to the ground.
- The distance the ball falls is the height of the hill, which is 6 meters.
- We can use the formula: distance = (1/2) * acceleration * time^2.
- Rearranging the formula, we get: time = sqrt(2 * distance / acceleration).
- Plugging in the values: time = sqrt(2 * 6 / 1.67).
Step 2: Find the horizontal distance the ball travels in that time.
- The horizontal distance traveled by the ball is given by the formula: distance = velocity * time.
- The velocity of the ball is given as 15 m/s.
- Plugging in the values: distance = 15 * sqrt(2 * 6 / 1.67).
Calculating the solution:
- Using a calculator, we evaluate the expression: distance = 15 * sqrt(2 * 6 / 1.67).
- The horizontal distance the ball strikes the ground is approximately 17.04 meters.
Therefore, the ball strikes the ground approximately 17.04 meters away from the point directly below the launch point.