BridgeMechanicsFree

Conversion in Front of the Posts

Projectiles and forces

In a club rugby match in Porirua, a kicker takes a conversion from a point on the ground directly in front of the posts,

32.0\ \text{m}

(measured horizontally) from the crossbar. The crossbar is

3.00\ \text{m}

above the ground. The ball leaves the ground with speed

u = 22.0\ \text{m s}^{-1}

\theta = 35.0^\circ

above the horizontal, travelling in a vertical plane perpendicular to the crossbar. Treat the ball as a particle and ignore air resistance and spin unless told otherwise.

Data: g = 9.81 m s⁻²

(a)

show that2 marks

Show that the height

y

of the ball at a horizontal distance

x

from the kicking point is

y = x\tan\theta - \dfrac{gx^2}{2u^2\cos^2\theta}

(b)

calculate2 marks

Determine whether the kick clears the crossbar, and by how much.

(c)

calculate2 marks

The kicker can always kick at

u = 22.0\ \text{m s}^{-1}

but can choose the launch angle. Calculate the range of launch angles for which the ball clears the crossbar from this position.

(d)

explain2 marks

In reality air resistance acts on the ball. Explain how air resistance changes the horizontal and vertical motion of the ball, and state which quantity that was constant in (a)–(c) is no longer constant. Explain whether your conclusion in (b) is still reliable.

Your score: 0 / 8(0 of 4 parts marked — open “Mark it” on each part)