A ball is thrown vertically upward with a velocity of 100m/s.It will reach the ground after hw many sec?
The total time in the air is twice the time it takes for the ball to decelerate to 0 m/s (at the mazximum height). That time equals 2Vo/g, where Vo is the initial velocity.
That would be 20.4 seconds.
The maximum height reached would be 1020 m. A human cannot throw a ball that fast. The question is unrealisttic. Aerodynamic resistance would be appreciable.
100 m/s is 328 miles/hour, nearly half the speed of sound.
Take the values....V=om/s..U=100m/s...a=g=-10m/s(since it is against the gravity)..t=?....Using 1st kinematic equation i.e. V=U+at...putting all the values....0=100+(-10)t... -100=-10t....t=-100/-10..t=+10 sec.....since total time equals time taken going up nad going down...therefore t=10+10.....t=20sec.
To determine the time it takes for the ball to reach the ground, we need to consider the motion of the ball and use the equation of motion.
Let's break down the problem into two parts: the ball's upward motion and its downward motion.
1. Upward Motion:
When the ball is thrown upward, its initial velocity (u) is +100 m/s because it is moving up against the force of gravity. The acceleration (a) due to gravity is -9.8 m/s² (negative because it acts downward). We need to find the time it takes for the upward motion to reach its maximum height (when the velocity becomes zero).
Using the equation of motion: v = u + at, where:
v = final velocity (which is 0 m/s at the highest point)
u = initial velocity (100 m/s)
a = acceleration (-9.8 m/s²)
t = time
0 = 100 - 9.8t
9.8t = 100
t = 100 / 9.8
t ≈ 10.2 seconds
Therefore, it takes approximately 10.2 seconds for the ball to reach its maximum height during its upward motion.
2. Downward Motion:
Once the ball reaches its maximum height, it starts to fall back to the ground. In this case, the initial velocity (u) is 0 m/s because it momentarily stops at the top before moving downward. The acceleration (a) due to gravity remains -9.8 m/s² (negative because it acts downward).
To find the time it takes for the ball to hit the ground, we use the same equation of motion: v = u + at, but now we need to find the time when the ball reaches the ground.
Since we know that it takes approximately 10.2 seconds to reach the maximum height, the total time for the ball to reach the ground will be twice that time, as the upward and downward motions take the same duration.
Total time = 2 * 10.2 seconds = 20.4 seconds
Hence, the ball will reach the ground after approximately 20.4 seconds.