A girl makes a jump in the long jump with an initial velocity of 12 m/s. She leaves the ground at 20 degrees above the horizontal. How far is her jump?
See my other answer. You posted this twice. I gave you the formula to use, but did not derive it. That is something you should do yourself.
The assumed takeoff speed is completely unrealistic, as I note in my other answer.
To find the distance of the girl's jump, we need to use the concept of projectile motion. In this case, the motion of the girl can be divided into two components: horizontal and vertical.
First, let's analyze the horizontal component. Since there are no external forces acting horizontally (assuming no air resistance), the girl's velocity in the horizontal direction remains constant throughout the jump. Therefore, we can calculate the horizontal distance using the formula:
Distance = Horizontal Velocity * Time
Since the horizontal velocity remains constant, we can use the initial horizontal velocity (12 m/s) as the horizontal velocity throughout the jump. So, the horizontal distance is:
Distance = 12 m/s * Time
Now, let's focus on the vertical component of motion. The girl's initial velocity in the vertical direction is given as 20 degrees above the horizontal. We can decompose this initial velocity into its vertical and horizontal components.
The initial vertical velocity (Vy) can be found using trigonometry. Since the angle is given in degrees, we need to convert it to radians:
θ (in radians) = θ (in degrees) * π / 180
θ = 20 * π / 180 = 0.349 radians
Now, we can find the vertical component of the initial velocity using the formula:
Vy = Initial Velocity * sin(θ)
Vy = 12 m/s * sin(0.349) ≈ 4.185 m/s
Next, we need to determine the time for the girl's jump. In projectile motion, the time of flight is the same for both the vertical and horizontal components. To find the time, we can use the formula:
Time = 2 * (Vertical Velocity) / g
Where g is the acceleration due to gravity (approximately 9.8 m/s²). Plugging in the values, we get:
Time = 2 * 4.185 m/s / 9.8 m/s² ≈ 0.854 seconds
Now, we can substitute this time value back into the horizontal distance formula:
Distance = 12 m/s * 0.854 seconds ≈ 10.25 meters
Therefore, the girl's jump is approximately 10.25 meters.