New Zealand
Level 8 - NCEA Level 3

# Applications of Parametric Equations

## Interactive practice questions

The position in metres of a projectile $t$t seconds after its launch is described by $x=55t$x=55t and $y=102t-17t^2$y=102t17t2.

a

Find the time $t$t at which the projectile returns to the ground.

b

Find the maximum horizontal distance covered by the projectile.

c

Find the maximum height reached by the projectile.

d

Find the rectangular equation for the path of the projectile.

Easy
Approx 8 minutes

A plane takes off by flying in a straight line from the origin at a constant speed of $109$109 metres per second. The graph shows the position of the plane at a particular point in its flight.

A search-and-rescue team has been dispatched to rescue an injured bushwalker who is $20$20 km east and $21$21 km north of their current location. They move straight toward the bushwalker at a steady pace of $58$58 km/h.

Rochelle is trying to swim to the other side of a $2.5$2.5 km wide river. She sets off at a constant pace swimming due east and reaches the other side after $30$30 minutes, but was dragged $1.5$1.5 km downstream by the strong current flowing due south.

### Outcomes

#### M8-1

Apply the geometry of conic sections

#### 91573

Apply the geometry of conic sections in solving problems