Question

. A 1 kg projectile is fired from a cannon with an initial kinetic energy of 104 J. The cannon has an elevation angle of 45◦. How far does the projectile go before striking the ground (neglect the air resistance)?

Answer 1

The projectile goes approximately 14.96 meters before striking the ground.

To find the horizontal range (R) of the projectile, use the kinematic equation for projectile motion:

R = v²sin2θ / g

Where:

- R is the horizontal range,

- v is the initial velocity of the projectile,

- θ is the launch angle,

- g is the acceleration due to gravity (9.8m/s²)

First the initial velocity (v) using the initial kinetic energy (KE

KE = 1/2mv²

Given that KE = 104

J and m = 1kg

Find (v):

104J = 1/2 x 1kg x v²

Solving for (v):

v²= (104J x 2) / 1kg

v² = 208J / kg

v² = √208J/kg

Substitute (v) and (θ) into the range equation:

R = 208J/kg) x sin(2 x 45°) / 9.8m/s²

R = (208 x √2/2) / 9.8

R = (104√2) / 9.8

Calculate the numerical value for (R):

R ≈ (104 x 1.4142) / 9.8

R ≈ 146.3668 / 9.8

R ≈ 14.96m

Therefore, the projectile goes approximately 14.96 meters before striking the ground.