First slide

Projection Under uniform Acceleration

Question

In the locus diagrams of two projectiles I and 2 as shown in the fig.,

Moderate

A

$T_{1} > T_{2} and v_{0_{1}} < v_{0_{2}}$
B

$T_{1} = T_{2} and v_{0_{1}} < v_{0_{2}}$
C

$T_{1} = T_{2} and v_{0_{1}} > v_{0_{2}}$
D

$T_{1} < T_{2} and v_{0_{1}} < v_{0_{2}}$

Solution

Both projectiles have same height.
$∴ H_{1} = H_{2}$
$\frac{{(u_{1} \sin θ_{1})}^{2}}{2 g} = \frac{{(u_{2} {sinθ}_{2})}^{2}}{2 g}$
$u_{1} \sin θ_{1} = u_{2} \sin θ_{2}$
$\frac{2 u_{1} \sin θ_{1}}{g} = \frac{2 u_{2} \sin θ_{2}}{g} \Rightarrow T_{1} = T_{2}$
Now $\frac{u_{1}}{u_{2}} = \frac{\sin θ_{2}}{\sin θ_{1}} \sin θ_{1} > θ_{2}$
$\frac{\sin θ_{1}}{\sin θ_{2}} > 1 \Rightarrow \frac{u_{1}}{u_{2}} < 1$

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