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

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 45

The velocity components of the projectile are given by the derivatives of the position coordinates with respect to time.

v_x = \dfrac{dx}{dt} = \dfrac{d}{dt}(24t) = 24

v_y = \dfrac{dy}{dt} = \dfrac{d}{dt}(43.6t - 4.9t^2) = 43.6 - 9.8t

At

t = 2

s, the velocity components are:

v_x = 24

v_y = 43.6 - 9.8(2) = 43.6 - 19.6 = 24

The angle

\theta

made by the velocity vector with the horizontal is given by:

\tan \theta = \dfrac{v_y}{v_x} = \dfrac{24}{24} = 1

\theta = 45^{\circ}

Answer:

45

If x and y coordinates of a projectile as a function of time (t)...

Options

Correct answer

Step-by-step solution

More from Motion in Two Dimensions