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Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

The objective is to help students understand what they are learning and develop the ability to solve problems they have not seen before.

Drone Power Failure

A small drone launched at an angle of $45^\circ$ with horizontal moves with constant velocity of $\sqrt {200}$ m/s. Its power shuts down just 4 second after the launch. Find the horizontal range of the drone. [Ignore air, $g=10 m/s^2$]

Solution

Motion with constant velocity

$d = ucos\theta.t = 40m$

$h = usin\theta.t = 40m$

Projectile motion

$y = -40 = usin\theta .t - \frac {1}{2} g t^2 = 10.t-\frac {1}{2}.10.t^2=10t-5t^2$

$\therefore 5t^2-10t-40=0$

$\Rightarrow t^2-2t-8=0$

$\Rightarrow (t-4)(t+2) = 0$, t = 4 sec

$R=ucos\theta .t=10.4 = 40 m$

Range = d+R = 40+40 m = 80 m