Suppose you throw a ball up in the air and it stops rising after 1.5 seconds. the initial speed of the ball is
6.2
In order to determine the initial speed of the ball, we can use the equation for vertical motion, which is given by:
h = v₀t + (1/2)gt²
where:
h is the vertical displacement (in this case, it would be 0 because the ball stops rising)
v₀ is the initial speed of the ball
t is the time it takes for the ball to reach its maximum height (in this case, 1.5 seconds)
g is the acceleration due to gravity (which is approximately -9.8 m/s²)
Since the ball stops rising at its maximum height, the displacement is 0, and the equation becomes:
0 = v₀(1.5) + (1/2)(-9.8)(1.5)²
Simplifying the equation, we have:
0 = 1.5v₀ - (1/2)(9.8)(1.5)²
0 = 1.5v₀ - 11.025
Rearranging the equation to solve for v₀, we get:
v₀ = 11.025 / 1.5
Calculating the value, we have:
v₀ ≈ 7.35 m/s
So, the initial speed of the ball is approximately 7.35 m/s.
To find the initial speed of the ball, we can use the kinematic equation for vertical motion:
v = u + gt
Where:
v = final velocity (which is 0 when the ball stops rising)
u = initial velocity (what we want to find)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time (1.5 seconds)
Rearranging the equation, we get:
u = v - gt
Now, since the ball stops rising, the final velocity (v) is 0. We can substitute this into the equation:
u = 0 - g * t
So, to find the initial speed of the ball, we need to multiply the acceleration due to gravity (g) by the time (t). In this case, the time is 1.5 seconds. Therefore, the formula becomes:
u = 0 - (9.8 m/s^2) * (1.5 s)
Simplifying the equation:
u = - 14.7 m/s
The negative sign indicates that the initial velocity is in the opposite direction to the motion, meaning the ball was thrown upward. Therefore, the initial speed of the ball is 14.7 m/s upward.