A tennis ball is shot vertically upward in an evacuated chamber inside a tower with an initial speed of 20.0 m/s at time t = 0 s.
Approximately how long does it take the tennis ball to reach its maximum height?
v = Vi - g t
0 = 20 - 9.81 t
t = about 2 seconds
Well, if the tennis ball is shot vertically upward in an evacuated chamber, I hope it doesn't get too lightheaded! Anyway, back to the question.
Since we're dealing with a vertical motion, we can use the formula:
time = initial velocity / acceleration
When the ball reaches its maximum height, its velocity will be 0 m/s. So, the initial velocity is 20.0 m/s. In this case, acceleration would be the acceleration due to gravity, which is approximately 9.8 m/s².
Plugging these values in, we get:
time = 20.0 m/s / 9.8 m/s²
And after a little bit of calculation, we find that the time it takes for the tennis ball to reach its maximum height is approximately 2.04 seconds.
So, you can say that it takes about 2.04 seconds for the tennis ball to reach its maximum height. Just be sure to watch out for any smacking sounds when it lands, or else it might be making a racquet! Have fun!
To find the time it takes for the tennis ball to reach its maximum height, we can use the equation of motion for an object in freefall:
v = u + at
Where:
- v is the final velocity (0 m/s at the maximum height),
- u is the initial velocity (20.0 m/s),
- a is the acceleration due to gravity (-9.8 m/s^2 in this case), and
- t is the time.
At the maximum height, the final velocity is 0 m/s, so we can rearrange the equation as follows:
0 = 20.0 - 9.8t
Solving for t:
9.8t = 20.0
t = 20.0 / 9.8
t ≈ 2.04 seconds
Therefore, it takes approximately 2.04 seconds for the tennis ball to reach its maximum height.
To calculate the time it takes for the tennis ball to reach its maximum height, we can use the kinematic equation for vertical motion:
h = h0 + v0t + (1/2)gt^2
where:
h = final height
h0 = initial height (which is 0 in this case as the ball is shot vertically upwards)
v0 = initial velocity
g = acceleration due to gravity (approximately -9.8 m/s^2 for downward motion)
In this case, since the ball is shot vertically upward, the acceleration due to gravity will act in the opposite direction of the ball's velocity.
When the ball reaches its maximum height, its vertical velocity will be zero. So we can set v = 0 in the equation:
0 = v0 - gt
Solving for time (t), we get:
t = v0 / g
Plugging in the values, we have:
t = 20.0 m/s / (-9.8 m/s^2) ≈ -2.04 seconds
Note: The negative sign indicates that the time is taken as the negative of the maximum height. In this case, we are only interested in the magnitude of time, so we ignore the negative sign.
Therefore, it takes approximately 2.04 seconds for the tennis ball to reach its maximum height.