<p>A trough is $8$ metres long and its cross-sectional ends are in the shape of an isosceles triangle whose width is $5$ metres and height is $2$ metres. It is held in the position as shown in the figure by stands of the same height. At time $t$ seconds, the height of the water in the trough is $h$ metres and the width of the water surface is $w$ metres. The trough is initially empty and water is being pumped in at a constant rate of 5m$^{3}$/s.</p>
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<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Show that $w=\frac{5}{2}h$. Hence find the volume of the water in the trough in terms of $h$.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">Find the rate of change of $h$ at $t=2$.</span></div><p style="text-align: right;">[3]</p></li></ol>
<p>From $t=2$, the rate at which water is being pumped into the trough is changed to $2h$ m$^{3}$ /s.</p>
<ol class="i-list" start="3"><li><div class="list-item-content"><span class="list-item-text">Find the total time taken for the trough to be completely filled.</span></div><p style="text-align: right;">[3]</p></li></ol>

A trough is $8$ metres long and its cross-sectional ends are in the shape of an isosceles triangle whose width is $5$ metres and height is $2$ metres. It is held in the position as shown in the figure by stands of the same height. At time $t$ seconds, the height of the water in the trough is $h$ metres and the width of the water surface is $w$ metres. The trough is initially empty and water is being pumped in at a constant rate of 5m$^{3}$/s.

Show that $w=\frac{5}{2}h$. Hence find the volume of the water in the trough in terms of $h$.

From $t=2$, the rate at which water is being pumped into the trough is changed to $2h$ m$^{3}$ /s.

AJC P1 Q5

AJC P1 Q5

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