Sure, The problem here is one of projectile motion. In this category of physics problems, an object is launched into the air and then falls back to the ground. The total path traveled by the object before it hits the ground is the question we're trying to answer.
The first step is to convert the launch angle from degrees to radians, since all the trigonometric functions in physics require angles to be in radians. Converting 40° to radians gives us approximately 0.698 radians.
To determine the horizontal distance that the ball will cover (also known as the range), we use the following equation of motion:
d = (v² sin(2θ)) / g,
where
- d is the horizontal distance,
- v is the initial velocity,
- θ is the launch angle in radians,
- g is the acceleration due to gravity, which is approximately 9.81 m/s².
In the formula, sin(2θ) is the sine of the double of the launch angle. This is a consequence of the parabolic trajectory of the ball.
Substituting our given values into the formula, we get
d = (10 m/s)² * sin(2*0.698 radians) / 9.81 m/s²,
which simplifies to approximately 10.04 m.
Therefore, the ball will travel around 10.04 m before hitting the ground.