A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the horizontal distance that the long jumper travels
To determine the horizontal distance that the long jumper travels, we need to find the horizontal component of the initial velocity.
The horizontal velocity (Vx) can be calculated using the formula:
Vx = V * cos(theta),
where V is the magnitude of the velocity and theta is the angle above the horizontal.
Let's substitute the given values into the formula:
V = 12 m/s,
theta = 28 degrees.
First, we need to convert the angle from degrees to radians, because trigonometric functions in most programming languages use radians.
To convert degrees to radians, we use the formula:
radians = degrees * pi/180.
Converting 28 degrees to radians:
theta_rad = 28 * pi/180.
Next, we can calculate the horizontal velocity:
Vx = 12 m/s * cos(theta_rad).
Finally, we can calculate the horizontal distance (d) traveled by the long jumper using the formula:
d = Vx * t,
where t is the time the jumper spends in the air. Since we don't have the time, we'll assume it to be the time of flight.
The time of flight (t) can be calculated using the formula:
t = 2 * V * sin(theta) / g,
where g is the acceleration due to gravity (9.8 m/s^2).
Substituting the given values into the formula:
t = 2 * 12 m/s * sin(theta_rad) / 9.8 m/s^2.
Now we have the value of t, and we can calculate the horizontal distance traveled by the long jumper:
d = Vx * t.
Let's substitute the calculated values into this equation and solve it to find the horizontal distance.