Question

What s the minimom ini hal veloaty a rockst must be firea t ablk 000 km oway . VsC angle for mar raye

Answer 1

Range in projectile motion is given by:

R = (V0^2*sin 2$\theta$)/g

Now for minimum velocity, projectile angle should be 45 deg, So that range can be maximum

$\theta$ = 45 deg

sin 2$\theta$ = sin (2*45 deg) = sin 90 deg = 1

V0 = initial velocity of projectile

g = gravitational acceleration = 9.81 m/sec^2

R = range of rocket = 1000 km = 10^6 m

So,

V0^2 = g*R/sin 2$\theta$ = g*R

V0 = sqrt (g*R)

V0 = sqrt (9.81*10^6)

V0 = 3132.1 m/sec = minimum velocity of rocket

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