An elementary student kicks a ball straight into the air with a velocity of 16 feet/sec. If acceleration due to gravity is −32 ft/sec2, how many seconds after it leaves his foot will it take the ball to reach its highest point? Assume the position at time t = 0 is 0 feet.
1.25
6
0.50
Cannot be determined<- my answer
To find the time it takes for the ball to reach its highest point, we can use the equation:
vf = vi + at
Where:
- vf is the final velocity (which is 0 when the ball reaches its highest point),
- vi is the initial velocity (given as 16 ft/sec),
- a is the acceleration due to gravity (-32 ft/sec^2), and
- t is the time.
Let's solve for t.
0 = 16 + (-32)t
Simplifying the equation:
-16 = -32t
Dividing both sides by -32:
t = (-16) / (-32)
t = 0.5
Therefore, it will take the ball 0.5 seconds to reach its highest point.
The correct answer is option 0.50.
To find the time it takes for the ball to reach its highest point, we need to determine when the velocity of the ball becomes zero.
We know that the velocity of the ball is decreasing due to gravity, so we can use the formula:
vf = vi + at
Where:
vf = final velocity (zero in this case, since the ball reaches its highest point and then starts descending)
vi = initial velocity (16 ft/sec)
a = acceleration due to gravity (-32 ft/sec^2)
t = time
Rearranging the formula to solve for time (t), we have:
t = (vf - vi) / a
Plugging in the values, we get:
t = (0 - 16) / -32 = 0.5 seconds
Therefore, it will take the ball 0.5 seconds to reach its highest point.
So, the correct answer is 0.50 seconds.
h(t) = 16t - 16t^2
surely you can find the vertex of a parabola.