A ball is thrown vertically upward, which is the positive direction. A little later it returns to its point of release. The ball is in the air for a total time of 7.84 s. What is its initial velocity? Neglect air resistance.
1.63
A ball is thrown vertically upward, which is the positive direction. A little later it returns to its point of release. The ball is in the air for a total time of
8.6 s.
What is its initial velocity? Neglect air resistance. (Indicate the direction with the sign of your answer.)
To find the initial velocity of the ball, we can use the equation of motion for vertical motion, also known as the equation of free fall.
The equation of motion for vertical motion is given by:
y = v₀t + (1/2)gt²
Where:
- y is the displacement (in this case, it is zero since the ball returns to its point of release),
- v₀ is the initial velocity,
- t is the time the ball is in the air, and
- g is the acceleration due to gravity.
Since the ball returns to its point of release, its displacement is zero. Thus, we can rewrite the equation as:
0 = v₀t + (1/2)gt²
To solve for v₀, we need to rearrange the equation and isolate v₀:
v₀ = -(1/2)gt
Given:
t = 7.84 s (the total time the ball is in the air),
g = 9.8 m/s² (acceleration due to gravity).
Substituting these values into the equation:
v₀ = -(1/2) * 9.8 m/s² * 7.84 s
Now we can calculate the initial velocity:
v₀ = -(1/2) * 9.8 m/s² * 7.84 s
v₀ = -38.4704 m/s (rounded to four decimal places, retaining the negative sign as it indicates the upward direction)
Therefore, the initial velocity of the ball is approximately -38.4704 m/s in the upward direction.