Question

A ball is thrown upward at time t = 0.0 s, from a point on a roof 60 m above the ground. The
ball rises, then falls and strikes the ground. The initial velocity of the ball is 28.4 m/s. Consider
all quantities as positive in the upward direction. At time t = 4.3 s, the acceleration of the ball is
closest to

Answer 1

Answer on Question #40907, Physics, Mechanics

A ball is thrown upward at time $t = 0.0$ s, from a point on a roof $60$ m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is $28.4$ m/s. Consider all quantities as positive in the upward direction. At time $t = 4.3$ s, the acceleration of the ball is closest to

Solution:

An object in free fall experiences an acceleration $g$ of $-9.81 \, \text{m/s}^2$. (The sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is $-9.8 \, \text{m/s}^2$ for any freely falling object.

The time of moving to the top point is

$$y = y_0 + v_0 t + \frac{1}{2} a t^2$$

where

$y_0 = 60 \, \text{m}$ is initial position

$v_0 = 28.4 \, \text{m/s}$ is initial speed

$a = g = -9.81 \, \text{m/s}^2$ is acceleration

At time $t = 4.3$ s, the position of a ball is

$$y = 60 + 28.4 \cdot 4.3 + \frac{1}{2} (-9.81) \cdot 4.3^2 = 91.4 \, \text{m}$$

That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of $9.81 \, \text{m/s}^2$. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is $-9.81 \, \text{m/s}^2$.

Answer. $-9.81 \, \text{m/s}^2$