A golf ball is struck from a point $O\,$ on level ground. Its position $t\,$ seconds after being struck is modelled by

$20t\cos\alpha$ , $20t\sin\alpha - 4.9t^2$

where $x\,$ metres and $y\,$ metres are the horizontal and vertical displacements from $O$ , and $\alpha\,$ is the angle of projection above the horizontal.

Show that a Cartesian equation for the path of the ball is

$y=xtan⁡α−49x2sec⁡2α4000\displaystyle y = x\tan\alpha - \frac{49x^2\sec^2\alpha}{4000}$

Given that $α=30°\alpha = 30°$ , find the horizontal distance travelled by the ball before it first returns to the ground. Give your answer to three significant figures.

State one modelling assumption that has been made.

A golf ball is struck from a point $O\,$ on level ground. Its position $t\,$ seconds after being struck is modelled by

$20t\cos\alpha$ , $20t\sin\alpha - 4.9t^2$

where $x\,$ metres and $y\,$ metres are the horizontal and vertical displacements from $O$ , and $\alpha\,$ is the angle of projection above the horizontal.

Show that a Cartesian equation for the path of the ball is

$y=xtan⁡α−49x2sec⁡2α4000\displaystyle y = x\tan\alpha - \frac{49x^2\sec^2\alpha}{4000}$

Given that $α=30°\alpha = 30°$ , find the horizontal distance travelled by the ball before it first returns to the ground. Give your answer to three significant figures.

State one modelling assumption that has been made.

1.6 C: Coordinate geometry in the (x, y) plane

Question 13

Markscheme

1.6 C: Coordinate geometry in the (x, y) plane

Question 13

Markscheme

1.6 C: Coordinate geometry in the (x, y) plane

Question 13

1.6 C: Coordinate geometry in the (x, y) plane Questions

1.6 C: Coordinate geometry in the (x, y) plane

Question 13

1.6 C: Coordinate geometry in the (x, y) plane Questions