a giant robot tosses a ball up, from a height of 80 meters, with an initial velocity of Vo = 60 m/s, use 10 m/s^2 as the acceleration due to gravity.
what will be the minimum velocity of the ball and when and where will that occur? [i don't know how you would find that.]
what will be the maximum speed, and when and where will that occur/
how many times can the ball attain a speed greater than 60 m/s but less that its maximum speed?
The velocity is the initial velocity + any velocity based on the acceleration of gravity. Gravity is a negative acceleration to an object thrown upwards. The minimum velocity will be where the ball stops going up and falls back down.
Where maximum speed occurs will depend on whether the robot catches the ball or it falls to his feet.
Use a(t)=-32 ft/s squared as the acceleration due to gravity. A ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second. For how many seconds will the ball be going upward?
A vehicle changes its velocity from 90 km/h to a dead stop in 10s. Show that its acceleration in doing so is -2.5m/s2
To find the minimum velocity of the ball and where it occurs, we can use the equations of motion. We know that the acceleration due to gravity is -10 m/s^2 since it acts in the opposite direction to the motion of the ball.
1. Find the time it takes for the ball to reach its minimum velocity:
Using the second equation of motion, we have:
Vf = Vo + at
0 = 60 - 10t
Solving for t, we get t = 6 seconds.
2. Determine the height at that time:
Using the first equation of motion, we can find the height:
h = Vo*t + (1/2)at^2
h = 60 * 6 + (1/2)(-10)(6^2)
h = 360 - 180
h = 180 meters
Therefore, the minimum velocity of the ball will occur after 6 seconds of flight, at a height of 180 meters.
To find the maximum speed and where it occurs, we need to find the time it takes for the ball to reach its peak.
3. Find the time it takes for the ball to reach its peak:
Using the first equation of motion, when the ball reaches its peak, its final velocity (Vf) will be 0. Therefore:
Vf = Vo + at
0 = 60 - 10t
Solving for t, we get t = 6 seconds (same as before).
To determine the maximum speed, we just need to take the absolute value of the initial velocity, since the ball will reach its peak with the same magnitude as its initial velocity.
Therefore, the maximum speed of the ball is 60 m/s, which occurs after 6 seconds of flight at the peak of its trajectory.
Now, to find the number of times the ball attains a speed greater than 60 m/s but less than its maximum speed:
4. Calculate the maximum speed:
We already know that the maximum speed is 60 m/s.
5. Find the height at which the ball attains a speed greater than 60 m/s:
Using the first equation of motion, we can calculate the height using the given time:
h = Vo*t + (1/2)at^2
h = 60 * 6 + (1/2)(-10)(6^2)
h = 360 - 180
h = 180 meters
Now we know that the ball reaches a height of 180 meters when its speed is greater than 60 m/s.
From the information given, we know that the minimum and maximum speeds occur at the same time (after 6 seconds). Therefore, the ball cannot attain a speed greater than 60 m/s but less than its maximum speed since they are the same.