In this question use g=9.8g = 9.8g=9.8 m s−2^{-2}−2.
A toy launcher shoots balls from ground level with an initial speed of 9 m s−1^{-1}−1.
The advertisement for the toy claims the balls can reach a maximum height of 4 metres above the ground.
Suppose the launcher shoots the balls vertically upwards. Verify the claim in the advertisement.
State two modelling assumptions you have made in verifying this claim.
In fact the launcher shoots the balls anywhere between 0° 0°\,0° and 12° 12°\,12° from the vertical. The range of maximum heights, h h\,h metres, above the ground which can be reached by the balls may be expressed as k≤h≤4.13k \le h \le 4.13k≤h≤4.13. Find the value of kkk.
260 exam-style questions on OCR A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Displacement-time and velocity-time graphs, 3.2.4 Constant acceleration formulae, 3.2.5 Constant acceleration in two dimensions (A-level only), 3.2.6 Non-uniform acceleration in one dimension (A-level only), 3.2.7 Non-uniform acceleration in two dimensions (A-level only), 3.2.8 Motion under gravity using vectors (A-level only), and 3.2.9 Projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.