1. No category

With what velocity must a ball be thrown vertically upward in order to

With what velocity must a ball be thrown vertically upward in order to rise a height of 50m? How
long will it be in the air?
Solution:
The equation of motion for the ball:
𝐻 = 𝑉𝑑 βˆ’
𝑔𝑑 2
(1),
2
𝑑 βˆ’ π‘“π‘™π‘–π‘”β„Žπ‘‘ π‘‘π‘–π‘šπ‘’ π‘‘π‘œ π‘Ÿπ‘’π‘Žπ‘β„Ž π‘‘β„Žπ‘’ β„Žπ‘’π‘–π‘”β„Žπ‘‘ 𝐻 = 50π‘š
Rate equation for the ball, in the end of the flight speed
of the ball is zero:
0 = 𝑉 βˆ’ 𝑔𝑑
𝑑=
𝑉
(2)
𝑔
(2)𝑖𝑛 (1): 𝐻 = 𝑉
𝐻=
𝑉 = √2𝑔𝐻 = √2 βˆ— 10
𝑉
βˆ’
𝑔
𝑉 2
𝑔 (𝑔 )
𝑉2
2𝑔
π‘š
π‘š
βˆ— 50π‘š = 31.6
2
𝑠
𝑠
Residence time in the air: time of flight of the ball upward equals time of the fall:
𝑇 = 𝑑𝑒𝑝 + π‘‘π‘‘π‘œπ‘€π‘›
Answer: velocity: 𝑉 = 31.6
Time in the air:𝑇 = 6.32 𝑠
π‘š
𝑠
π‘š
2𝑉 2 βˆ— 31.6 𝑠
= 2𝑑 =
=
= 6.32 𝑠
π‘š
𝑔
10 2
𝑠
2

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