CAIE M2 2014 June — Question 4

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2014
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProjectiles
TypeSpeed at specific time or position
DifficultyStandard +0.8 This projectile question requires energy methods or component analysis to find height from speed (non-standard), then solving for two time instances when speed equals 18 m/s. Part (ii) demands finding the time interval and corresponding horizontal distance, requiring careful manipulation of projectile equations beyond routine trajectory problems.
Spec3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model

4 A particle \(P\) is projected with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(40 ^ { \circ }\) above the horizontal from a point \(O\) on horizontal ground.
  1. Find the height of \(P\) above the ground when \(P\) has speed \(18 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  2. Calculate the length of time for which the speed of \(P\) is less than \(18 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and find the horizontal distance travelled by \(P\) during this time.

4 A particle $P$ is projected with speed $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $40 ^ { \circ }$ above the horizontal from a point $O$ on horizontal ground.\\
(i) Find the height of $P$ above the ground when $P$ has speed $18 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(ii) Calculate the length of time for which the speed of $P$ is less than $18 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, and find the horizontal distance travelled by $P$ during this time.

\hfill \mbox{\textit{CAIE M2 2014 Q4}}