Answer:
Explanation:
We should first find the velocity and acceleration functions. The velocity function is the derivative of the position function with respect to time, and the acceleration function is the derivative of the velocity function with respect to time.
Similarly,
Now, the angle between velocity and acceleration vectors can be found.
The angle between any two vectors can be found by scalar product of them:
So,
At time t = 0, this equation becomes
Answer:
The initial velocity of the softball is 14.711 meters per second.
Explanation:
This is a case of an object which experiments a free fall, that is, an uniform accelerated motion due to gravity and in which effects from air friction and Earth's rotation can be neglected.
From statement we must understand that the student threw the softball upwards and it is caught at original position 3.56 seconds later. Initial and final heights, time and gravitational acceleration are known and initial speed is unknown. The following equation of motion is used:
(Eq. 1)
Where:
- Initial height of the softball, measured in meters.
- Final height of the softball, measured in meters.
- Initial velocity of the softball, measured in meters per second.
- Time, measured in seconds.
- Gravitational acceleration, measured in meters per square second.
If we know that ,
and
, the initial velocity of the softball is:
The initial velocity of the softball is 14.711 meters per second.