Question 10: Motion in 2D & Vectors

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 $t=2 \mathrm{~s}$ is $\_\_\_\_$ .

Accepted Answer

For a projectile, the angle it makes with the horizontal at any instant is found from the velocity components.
Given:
$$ x=24t $$
and
$$ y=43.6t-4.9t^2 $$
So, horizontal velocity is
$$ v_x=\frac{dx}{dt}=24 $$
and vertical velocity is
$$ v_y=\frac{dy}{dt}=43.6-9.8t $$
At $t=2	ext{ s}$,
$$ v_y=43.6-9.8(2)=43.6-19.6=24 $$
Thus,
$$ 	an 	heta=\frac{v_y}{v_x}=\frac{24}{24}=1 $$
So,
$$ 	heta=45^\circ $$
Hence, the correct answer is:
$$ \boxed{45^\circ} $$
Option B

Answer

60

Answer

45

Answer

30

Answer

75

Motion in 2D & Vectors

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 \mathrm{~s} is \_\_\_\_ .

Choose the correct answer: