Graphs 4
4 marks · HardA projectile is launched so that its height, metres, above the ground after seconds is given by .
Find the maximum height reached by the projectile and the time at which it occurs.
Determine the time when the projectile returns to the ground.
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.).