Answer:
1.a) 3.93 m/s
b) 0.80 s
2. a) 8.49 m
b) 0.39 s
Explanation:
1. a) The speed at which the fox leaves the snow can be found as follows:
![v_{f}^{2} = v_{0}^{2} - 2gH](https://tex.z-dn.net/?f=%20v_%7Bf%7D%5E%7B2%7D%20%3D%20v_%7B0%7D%5E%7B2%7D%20-%202gH%20)
Where:
g: is the gravity = 9.80 m/s²
: is the final speed = 0 (at the maximum height)
: is the initial speed =?
H: is the maximum height = 79 cm = 0.79 m
![v_{0} = \sqrt{2gH} = \sqrt{2*9.80 m/s^{2}*0.79 m} = 3.93 m/s](https://tex.z-dn.net/?f=%20v_%7B0%7D%20%3D%20%5Csqrt%7B2gH%7D%20%3D%20%5Csqrt%7B2%2A9.80%20m%2Fs%5E%7B2%7D%2A0.79%20m%7D%20%3D%203.93%20m%2Fs%20)
Hence, the speed at which the fox leaves the snow is 3.93 m/s.
b) The time at which the fox reaches the maximum height is given by:
![v_{f} = v_{0} - gt](https://tex.z-dn.net/?f=v_%7Bf%7D%20%3D%20v_%7B0%7D%20-%20gt)
![t = \frac{v_{0} - v_{f}}{g} = \frac{3.93 m/s}{9.80 m/s^{2}} = 0.40 s](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bv_%7B0%7D%20-%20v_%7Bf%7D%7D%7Bg%7D%20%3D%20%5Cfrac%7B3.93%20m%2Fs%7D%7B9.80%20m%2Fs%5E%7B2%7D%7D%20%3D%200.40%20s)
Now, the time of flight is:
![t_{v} = 2t = 2*0.40 s = 0.80 s](https://tex.z-dn.net/?f=%20t_%7Bv%7D%20%3D%202t%20%3D%202%2A0.40%20s%20%3D%200.80%20s%20)
2. a) The maximum height the ball reaches is:
![H = \frac{v_{0}^{2} - v_{f}^{2}}{2g} = \frac{(12.9 m/s)^{2}}{2*9.80 m/s^{2}} = 8.49 m](https://tex.z-dn.net/?f=%20H%20%3D%20%5Cfrac%7Bv_%7B0%7D%5E%7B2%7D%20-%20v_%7Bf%7D%5E%7B2%7D%7D%7B2g%7D%20%3D%20%5Cfrac%7B%2812.9%20m%2Fs%29%5E%7B2%7D%7D%7B2%2A9.80%20m%2Fs%5E%7B2%7D%7D%20%3D%208.49%20m%20)
Then, the maximum height is 8.49 m.
b) The time at which the ball passes through half the maximum height is:
![y_{f} = y_{0} + v_{0}t - \frac{1}{2}gt^{2}](https://tex.z-dn.net/?f=y_%7Bf%7D%20%3D%20y_%7B0%7D%20%2B%20v_%7B0%7Dt%20-%20%5Cfrac%7B1%7D%7B2%7Dgt%5E%7B2%7D)
Taking y₀ = 0 and
= 8.49/2 = 4.245 m we have:
By solving the above quadratic equation we have:
t = 0.39 s
Therefore, the time at which the ball passes through half the maximum height when the ball is going up is 0.39 s.
I hope it helps you!