Graphs 4

4 marks · Hard

A projectile is launched so that its height, metres, above the ground after seconds is given by .

(a)

Find the maximum height reached by the projectile and the time at which it occurs.

[3 marks]

(b)

Determine the time when the projectile returns to the ground.

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) Maximum height is 22 m at t = 2 s m, s

(b) At t = 5 s

Common mistakes: Incorrect use of quadratic formula; Finding a minimum instead of maximum

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Find the value of t for maximum using

A1 (a) · 1 mark · Correct value of t = 2 (follow-through)

A2 (a) · 1 mark · Correct height at t = 2: 22 m (follow-through)

M2 (b) · 1 mark · Set h = 0 and solve quadratic for time.

Worked solution

The height is given by .

(a) The maximum height occurs at the vertex: seconds.

Substitute into the equation: . Correction: . Oops, redo:

Thus, the maximum height is 14 m at t = 2 s.

(b) The projectile returns to the ground when . Solve .

Using the quadratic formula:

So we have two times: (to 3 s.f.), and , negative time is not valid.

So the projectile hits the ground at t = 4.65 s (to 2 d.p.).