2022 TMJC P1 Q10
A squirrel falls vertically from a tall tree. The distance, $x$ metres, that the squirrel has fallen from the tree after $t$ seconds is observed. It is given that $x=0$ and $\frac{\text{d}x}{\text{d}t}=0$ when $t=0$.
The motion of the squirrel is modelled by the differential equation
$\frac{{{\text{d}}^{2}}x}{\text{d}{{t}^{2}}}+0.1{{\left( \frac{\text{d}x}{\text{d}t} \right)}^{2}}=10$.
(i)
By substituting $y=\frac{\text{d}x}{\text{d}t}$, show that the differential equation can be written as $\frac{\text{d}y}{\text{d}t}=10-0.1{{y}^{2}}$.
[1]
(ii)
Find $y$ in terms of $t$ and hence find $x$ in terms of $t$.
[8]
(iii)
How far has the squirrel fallen after $2$ seconds?
[1]
(iv)
For a falling object, the terminal velocity is the value approached by the velocity after a long time. Find the terminal velocity of the falling squirrel.
[2]
Suggested Video Solutions
Our H2 Math Tuition includes
- Question Bank with Video solutions to 1400+ questions
- Online Portal
- H2 Math Summary Notes
- Structured Curriculum and Notes
Share with your friends!
Continue reading
5 Exam Preparation Tips: How We Help Students Excel in Exams
In the ever-evolving landscape of education, where academic success is often measured by performance in exams, the need for effective test preparation has never been more critical. Students face a
List MF 27
What is the MF 27? The MF 27, set to replace the MF 26 from 2025, is a comprehensive formula sheet developed by the Ministry of Education Singapore in collaboration
Panic No More: What To Do The Day Before An Exam?
As you approach the final hours before your exam, remember that a balanced approach is key. A light review can keep the information fresh in your mind, while preparing your