If and coordinates of a projectile as a function of time are given as and , respectively, then the angle (in degrees)

Question

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24 t$ and $43.6 t - 4.9 t^{2}$ , respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2 s$ is ________. [2026]

Smart Achievers · Accepted Answer

(2)

$x = 24 t, y = 43.6 t - 4.9 t^{2}$

$v_{x} = \frac{d x}{d t} = 24$

$v_{y} = \frac{d y}{d t} = 43.6 - 9.8 t$

$at t = 2 sec.$

$\tan θ = \frac{v_{y}}{v_{x}} = \frac{24}{24} = 1 \Rightarrow θ = 45 °$

Solution

Q.
If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24 t$ and $43.6 t - 4.9 t^{2}$ , respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2 s$ is ________. [2026]

1 60

2 45

3 30

4 75

Ans.
(2)

$x = 24 t, y = 43.6 t - 4.9 t^{2}$

$v_{x} = \frac{d x}{d t} = 24$

$v_{y} = \frac{d y}{d t} = 43.6 - 9.8 t$

$at t = 2 sec.$

$\tan θ = \frac{v_{y}}{v_{x}} = \frac{24}{24} = 1 \Rightarrow θ = 45 °$

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