Aroldis Chapman throws a baseball towards a batter from a height of 2.3 m, the batter is 17.5m away from the release point. The initial velocity is directed 1.8 degrees below the horizontal.

Ignore air resistance.
(a) What must the initial speed of the ball be if the pitch is to arrive at the batter exactly 1.00 m above the ground?
(b) How long does it take the ball to reach the batter?
(c) If there were no gravity, at what angle would the pitch have to be thrown?

40.6 m/s

1.3 s
-26 degrees

actually, you are wrong brian. it is 47.34 m/s idiot. wow you are dumb. How could you even get that answer?

Joel is right.

I'm with his lab partner here.

Brian is right.

can anyone explain how they got their answer?

To solve this problem, we need to break it down into several parts. Let's start by finding the initial speed of the ball.

(a) What must the initial speed of the ball be if the pitch is to arrive at the batter exactly 1.00 m above the ground?

To find the initial speed, we can use the equations of motion. The equation we need for vertical motion is:

y = y0 + v0y * t - (1/2) * g * t^2

In this equation, y is the final vertical displacement, y0 is the initial vertical displacement, v0y is the initial vertical velocity, t is the time, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Using this equation, we can solve for the initial vertical velocity, v0y, when the ball is 1 m above the ground. We know that y0 = 2.3 m, y = 3.3 m (1 m above the ground), and g = 9.8 m/s^2.

Plugging the values into the equation, we get:

3.3 = 2.3 + v0y * t - (1/2) * 9.8 * t^2

Simplifying the equation, we have:

1 = v0y * t - 4.9 * t^2

Now, we also know that the horizontal displacement, x, is 17.5 m. We can use this information to find the time of flight, t, using the equation:

x = v0 * cos(theta) * t

In this equation, v0 is the initial speed of the ball and theta is the launch angle below the horizontal (1.8 degrees).

Plugging in the values, we have:

17.5 = v0 * cos(1.8 degrees) * t

Now we have two equations with two unknowns (v0y and t). We can solve these equations simultaneously to find the values.

Let's start by solving the second equation for t:

t = 17.5 / (v0 * cos(1.8 degrees))

Now we can substitute this value of t into the first equation:

1 = v0y * (17.5 / (v0 * cos(1.8 degrees))) - 4.9 * (17.5 / (v0 * cos(1.8 degrees)))^2

Simplifying this equation will give us the value of v0y. After finding v0y, we can find v0 using the equation:

v0 = v0y / sin(theta)

(b) How long does it take the ball to reach the batter?

Once we have the values of v0 and t, we can use the time of flight equation:

t = 17.5 / (v0 * cos(1.8 degrees))

(c) If there were no gravity, at what angle would the pitch have to be thrown?

If there were no gravity, the ball would follow a projectile motion path in a straight line. In this case, the ball would be thrown horizontally, and the angle would be 0 degrees.