Question

Madison throws a baseball horizontally from a height of 2.3m and wants 1 to get the ball to from the pitching mound to home plate which is a horizontal distance of 30m. How fast does he need to throw the ball to reach the plate?

A) 44m/s
B) 33m/s
C) 22m/s
D) 11m/s

Answer 1

Madison must throw the baseball at a speed very close to 44m/s to cover a horizontal distance of 30m while accounting for the gravitational drop over a height of 2.3m, calculated using projectile motion equations.

Step-by-step explanation:

To determine how fast Madison must throw the baseball to cover a horizontal distance of 30m, we first need to calculate the time it takes for the ball to fall from a height of 2.3m due to gravity, ignoring air resistance. This is a physics problem dealing with projectile motion where the horizontal and vertical motions are independent.

Using the kinematic equation for free fall, h = 1/2gt^2, where h is the height, g is the acceleration due to gravity (9.8 m/s2), and t is the time in seconds. We solve for t:

• 2.3m = 1/2(9.8m/s2)*t2
• t2 = 2*2.3m / 9.8m/s2
• t = sqrt(4.6/9.8)
• t ≈ 0.69s

To reach the horizontal distance of 30m in the same time, we use the formula for constant velocity, distance = velocity * time. Therefore, we calculate the velocity needed:

• 30m = velocity * 0.69s
• velocity = 30m / 0.69s
• velocity ≈ 43.48m/s

To the nearest whole number, the velocity required is approximately 44m/s. Therefore, Madison needs to throw the baseball at a speed very close to 44m/s (Option A) to reach home plate from the pitching mound.