Standard +0.3 This is a straightforward kinematics problem requiring application of SUVAT equations to two objects with different initial conditions. Students must set up two equations (one for each stone) and use the constraint that they land simultaneously. The algebra is routine and the problem type is standard M1 fare, making it slightly easier than average.
The points \(P\) and \(Q\) are at the same height \(h\) metres above horizontal ground. A small stone is dropped from rest from \(P\). Half a second later a second small stone is thrown vertically downwards from \(Q\) with speed 7.35 m s\(^{-1}\). Given that the stones hit the ground at the same time, find the value of \(h\). [7]
$h = \frac{1}{2}gt^2$ | B1 |
$h = 7.35(t - \frac{1}{2}) + \frac{1}{2}g(t - \frac{1}{2})^2$ | M1 A1 |
$\frac{1}{2}gt^2 = 7.35(t - \frac{1}{2}) + \frac{1}{2}g(t - \frac{1}{2})^2$ | DM1 |
$t = 1$ | M1 A1 |
$h = 4.9$ | A1 |
**Notes for Question 4:**
B1 for $h = \frac{1}{2}gt^2$ or $h = \frac{1}{2}g(t + \frac{1}{2})^2$
First M1 for $h = 7.35(t - \frac{1}{2}) + \frac{1}{2}g(t - \frac{1}{2})^2$ or $h = 7.35t + \frac{1}{2}gt^2$
M0 if different $t$ used in the two terms and M0 if two terms have opposite signs.
First A1 for appropriate $t$ value used
Second M1, dependent, for equating their two expressions for $h$, but must have different $t$'s in the two expressions
Third M1, independent, for solving for their $t$ (must have used two expressions etc.)
Second A1 for $t = 1$ (or $t = 1/2$)
Third A1 for $h = 4.9$
**Alternative approaches where $t$ is eliminated:**
$h = \frac{1}{2}gt^2$ | B1 |
$h = 7.35(t - \frac{1}{2}) + \frac{1}{2}g(t - \frac{1}{2})^2$ | M1A1 |
$h = 7.35(\sqrt{\frac{2h}{g}} - \frac{1}{2}) + \frac{1}{2}g(\sqrt{\frac{2h}{g}} - \frac{1}{2})^2$ | DM1 |
$h = 7.35(\frac{\sqrt{2h}}{k} - \frac{1}{2}) + \frac{1}{2}g(\frac{\sqrt{2h}}{k} - \frac{1}{2})^2$ | A1 |
$h = 4.9$ | M1 A1 |
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The points $P$ and $Q$ are at the same height $h$ metres above horizontal ground. A small stone is dropped from rest from $P$. Half a second later a second small stone is thrown vertically downwards from $Q$ with speed 7.35 m s$^{-1}$. Given that the stones hit the ground at the same time, find the value of $h$. [7]
\hfill \mbox{\textit{Edexcel M1 2015 Q4 [7]}}