# Maximum height

A rugby ball is kicked at the optimum angle to achieve the maximum possible range

Rmax for a given launching speed u. The ball experiences no air resistance and travels

along a parabolic path. What is the maximum height reached by the ball?

A 2Rmax B Rmax C Rmax/2 D Rmax/3 E Rmax/4

F Impossible to answer because the mass of the ball is unknown

G Impossible to answer because the launching angle is unknown

H impossible to answer because the launching speed is unknown

### 2 個解答

• 最愛解答

Optimum angle is 45˚

Horizontal speed, uH = ucos45˚ ms-1

Initial vertical speed, uV = usin45˚ ms-1

Assume time t is the time of flight

Horizontal range, utcos45˚ = Rmax

t = Rmax / ucos45˚ s

For maximum height, t’ = t/2 = Rmax / 2ucos45˚ = √2 Rmax / 2u s

By equation of motion,

v = uV – gt’

0 = ucos45˚ - 10(√2 Rmax / 2u)

u2 = 10Rmax ms-1

By equation of motion,

v2 = uV2 – 2gs

0 = (usin45˚)2 – 2(10)s

s = u2 / 40 = Rmax / 4

So, the answer is E. Maximum height is Rmax / 4.

資料來源： Myself~~~
• C Rmax/2

since the range is Rmax and we know intuitively that the max height will occur at the middle of Rmax ,which is Rmax/2 ..with the optimum angle which is usually 45degree, the calulated height will be Rmax/2 (by trigonometry)