Question

The following graphs show the horizontal position versus the vertical position for different projectiles based on the colors of the projectiles (air resistance negligible). All projectiles are launched from the same horizontal surface, under the same conditions.
What is the rank for the projectile for the time they spend in the air (greatest first)?

• A. Red and yellow tie, green, blue, purple
• B. Red, purple and green tie, blue and yellow tie
• C. Red, yellow, green, blue, purple
• D. Purple, red, green, blue, yellow
• E. Not enough information is given to answer this question

Answer 1

The correct option is D Purple, red, green, blue, yellow

Maximum height attained $H=\frac{u^{2}si{n}^2\theta }{2g}$ $⟹usin\theta =\sqrt{2gH}$

Time of flight $T=\frac{2usin\theta }{g}=\frac{2\sqrt{2gH}}{g}=2\sqrt{\frac{2H}{g}}$

$⟹$ $T\propto \sqrt{H}$

From figure, $H_{purple}>H_{red}>H_{green}>H_{blue}>H_{yellow}$

$⟹$ $T_{purple}>T_{red}>T_{green}>T_{blue}>T_{yellow}$