a ball of mass 4kg is thrown vertically upwards with a velocity of 40m/s.Find
a-maximum height
b-height after 3 seconds
c-time of flight
(a) Maximum height H is where the potential energy M g H equals the initial kinetic energy, (M/2)Vo^2.
Thus H = Vo^2/(2g)
(b) y(t) = Vo*t - (g/2) t6^2
Plug in t = 3.
(c) Twice as long as it takes for velocity to go from Vo to 0.
To find the answers to the given questions, we can use the equations of motion.
a) Maximum height:
To find the maximum height reached by the ball, we need to find the time it takes for the ball to reach its peak and then use that time to calculate the height.
Step 1: Find the time taken to reach maximum height (t):
Using the equation: v = u + at
Where:
v = final velocity = 0 m/s at maximum height
u = initial velocity = 40 m/s
a = acceleration due to gravity = -9.8 m/s^2 (negative sign because it acts in the opposite direction to the motion)
0 = 40 - 9.8t
t = 40/9.8 ≈ 4.08 seconds
Step 2: Calculate the maximum height (h):
Using the equation: s = ut + (1/2)at^2
Where:
s = displacement or height
u = initial velocity = 40 m/s
t = time taken to reach maximum height = 4.08 seconds
a = acceleration due to gravity = -9.8 m/s^2
h = 40(4.08) + (1/2)(-9.8)(4.08)^2
h ≈ 83.27 meters
Therefore, the maximum height reached by the ball is approximately 83.27 meters.
b) Height after 3 seconds:
To find the height after 3 seconds, we can use the same equation as above.
Using the equation: s = ut + (1/2)at^2
Where:
s = displacement or height
u = initial velocity = 40 m/s
t = time = 3 seconds
a = acceleration due to gravity = -9.8 m/s^2
h = 40(3) + (1/2)(-9.8)(3)^2
h ≈ 45.9 meters
Therefore, the height of the ball after 3 seconds is approximately 45.9 meters.
c) Time of flight:
The time of flight is the total time taken for the ball to reach the highest point and then fall back to the ground. To find it, we need to double the time it takes for the ball to reach maximum height.
Time of flight = 2 * time taken to reach maximum height
Time of flight = 2 * 4.08
Time of flight ≈ 8.16 seconds
Therefore, the time of flight for the ball is approximately 8.16 seconds.