Un proyectil es disparado horizontalmente con una angulo de tiro de 30 grados y una velocidad inicial de 850 metros por segundo. Calcular El tiempo de vuelo, altura máxima, alcance horizontal, posición a los 25 segundos, velocidad resultante a los 25 segundos

A) 86.7s

B) 9,215.56m

C) 63821.74m

D) 18402.5m

E) 757.79m/s

Explanation:

Given the following :

Angle of projection (Θ) = 30°

Initial Velocity (u) = 850m/s

g = acceleration due to gravity = 9.8m/s^2

A) The time of flight (T)

(2 × u × SinΘ) / g

(2 × 850 × sin30) / 9.8

(2 × 850 × 0.5) / 9.8

= 850 / 9.8 = 86.7seconds

B) Maximum height(H)

H = (u^2 × sin^2Θ) / 2g

H = (850^2 × 0.5^2) / 2 × 9.8

H = 180,625 / 19.6

H = 9215.5612m = 9,215.56m

C) horizontal range :

u × cosΘ × Time of fligt(T)

850 × cos30 × 86.7

850 × 0.866 × 86.7

= 63821.742m

D) position at 25 seconds

Distance = Speed × time

Distance at 25s = u × cosΘ × 25

= 850 × 0.866 × 25

= 18402.5m

E) Resulting Speed at 25s

Speed = distance / time

18402.5 / 25

Horizontal = 736.1 m/s

Vertical speed:

v = u + at

v = 850(sin30) + (-9.8 × 25)

v = 425 - 245

v = 180 m/s

Resulting speed :

V = √180^2 + 736.1^2

V = 757.78836m/s