Answer:
The displacement, velocity and time is 20.4 m, -4.52 m/s and 3.624 sec.
Explanation:
Given that,
Initial velocity =15.0 m/s
Height = 10 m
We need to calculate the displacement at 2 sec
Using equation of motion
![s=ut-\dfrac{1}{2}gt^2+s_{0}](https://tex.z-dn.net/?f=s%3Dut-%5Cdfrac%7B1%7D%7B2%7Dgt%5E2%2Bs_%7B0%7D)
Put the value into the formula
![s=15t-\dfrac{1}{2}\times9.8\times t^2+10](https://tex.z-dn.net/?f=s%3D15t-%5Cdfrac%7B1%7D%7B2%7D%5Ctimes9.8%5Ctimes%20t%5E2%2B10)
At 2 sec,
![s=15\times2-\dfrac{1}{2}\times9.8\times4+10](https://tex.z-dn.net/?f=s%3D15%5Ctimes2-%5Cdfrac%7B1%7D%7B2%7D%5Ctimes9.8%5Ctimes4%2B10)
![s=20.4\ m](https://tex.z-dn.net/?f=s%3D20.4%5C%20m)
We need to calculate the time
Using equation of motion again
![s=15t-\dfrac{1}{2}\times9.8\times t^2+10](https://tex.z-dn.net/?f=s%3D15t-%5Cdfrac%7B1%7D%7B2%7D%5Ctimes9.8%5Ctimes%20t%5E2%2B10)
At ground s = 0,
![15t-\dfrac{1}{2}\times9.8\times t^2+10=0](https://tex.z-dn.net/?f=15t-%5Cdfrac%7B1%7D%7B2%7D%5Ctimes9.8%5Ctimes%20t%5E2%2B10%3D0)
![4.9t^2-15t-10=0](https://tex.z-dn.net/?f=4.9t%5E2-15t-10%3D0)
![t = 3.624\ sec](https://tex.z-dn.net/?f=t%20%3D%203.624%5C%20sec)
Neglect the negative term because the time is not negative
We need to calculate the velocity
Using formula of velocity
![v=u-gt](https://tex.z-dn.net/?f=v%3Du-gt)
![v=15-9.8\times3.624](https://tex.z-dn.net/?f=v%3D15-9.8%5Ctimes3.624)
![v=-4.52\ m/s](https://tex.z-dn.net/?f=v%3D-4.52%5C%20m%2Fs)
Hence, The displacement, velocity and time is 20.4 m, -4.52 m/s and 3.624 sec.