Question

a projectile is launched over level ground with a speed of 240 m/s at 30° to the horizontal. if friction is negligible what is the height of the projectile 4s after launch?

Answer 1

a projectile is launched over level ground with a speed of 240m/s at an angle 30° to the horizontal.

so, initial velocity of projectile , $\vec{u}=240cos30^{\circ}\hat{i}+240sin30^{\circ}\hat{j}$

= $120\sqrt{3}\hat{i}+120\hat{j}$

hence, initial velocity of projectile in vertical direction is 120m/s and initial velocity in horizontal direction is 120√3 m/s.

you know, acceleration along vertical direction is acceleration due to gravity.

now using formula, h = ut - 1/2(g)t²

here, t = 4s , u = 120m/s, g = 10m/s²

then, h = 120 × 4 - 1/2 × 10 × (4)²

= 480m - 80m

= 400m

hence, height of projectile 4s after launch will be 400m