A ball is tossed straight up into the air with an initial velocity of +15 m/s and at a height (from where it leaves the thrower's hand) of 2.0 m off the ground. Once the ball leaves the thrower's hand, it accelerates at -9.8m/s/s.

a) How much does it take for the ball to hit the ground?

b) What is the highest position reached by the ball?

c) What is the acceleration of the ball at its highest point?

a) h=hi+vi*time - 4.9 t^2

solve for time
b) divide that time by 2, then figure height, same equation.

c) acceleration everywhere is the same, due to gravity.

To find the answers to the given questions, we can use the equations of motion.

a) To determine how long it takes for the ball to hit the ground, we need to calculate the time it takes for the ball to reach a height of 0m. We can use the equation:

d = v0 * t + (1/2) * a * t^2

where:
d = displacement (0m since it reaches the ground)
v0 = initial velocity (+15 m/s)
a = acceleration (-9.8 m/s^2)
t = time

Plugging in the known values, we have:

0 = 15 * t + (1/2) * (-9.8) * t^2

Simplifying the equation gives:

0 = 15t - 4.9t^2

Rearranging the equation to make it a quadratic equation:

4.9t^2 - 15t = 0

Solving this equation, we get two possible solutions:

t = 0s or t = 3.06s

Since time cannot be negative in this context, the ball takes approximately 3.06 seconds to hit the ground.

b) To find the highest position reached by the ball, we can use the equation for displacement:

d = v0 * t + (1/2) * a * t^2

We need to calculate the displacement at the highest point, which occurs when the velocity becomes 0. We know that the initial velocity is +15 m/s, the acceleration is -9.8 m/s^2, and we just found that the time it takes to hit the ground is approximately 3.06 seconds.

Plugging in the values, we have:

d = 15 * 3.06 + (1/2) * (-9.8) * (3.06)^2

Simplifying the equation gives:

d ≈ 46.0m

Therefore, the highest position reached by the ball is approximately 46.0 meters.

c) At the highest point of the ball's trajectory, the acceleration is equal to the acceleration due to gravity, which is -9.8 m/s^2. Gravity acts in the downward direction, so the acceleration is negative.