A long jumper leaves the ground at an angle of 20 degrees above horizontal and at a speed of 11m/s..how far does he jump?
time in air:
hf=ho+vo*sin20*t-4.9t^2
hf,ho=0, vo given 11m/s solve for time.
Now, how far
d=voCos20*time
To find out how far the long jumper jumps, we need to break down the given information and apply some physics concepts. Let's start step by step:
1. Identify the given values:
- Angle of takeoff (θ) = 20 degrees (above the horizontal)
- Initial speed (v0) = 11 m/s
2. Analyze the motion:
The long jumper experiences a projectile motion, which can be separated into horizontal and vertical components. The horizontal component remains constant since there is no acceleration in that direction. The vertical component is influenced by gravity.
3. Determine the initial velocity components:
We need to find the horizontal and vertical components of the initial velocity (v0x and v0y). The vertical component is given by v0y = v0 * sin(θ), and the horizontal component is v0x = v0 * cos(θ). Here, sin(θ) refers to the trigonometric sine function and cos(θ) refers to the trigonometric cosine function.
Substituting the values:
- v0y = 11 m/s * sin(20°)
- v0x = 11 m/s * cos(20°)
Calculate the values using a scientific calculator, and we get:
- v0y ≈ 3.74 m/s
- v0x ≈ 10.4 m/s
4. Calculate the time of flight:
The time of flight (t) refers to the total time taken by the long jumper to complete the jump and return to the ground. Since the vertical component is influenced by gravity, we can use the formula:
t = (2 * v0y) / g
Here, g refers to the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the value:
- t = (2 * 3.74 m/s) / 9.8 m/s²
Calculate the value, and we get:
- t ≈ 0.763 seconds
5. Calculate the horizontal distance:
The horizontal distance (d) traveled by the long jumper can be found by multiplying the horizontal component of the initial velocity (v0x) by the time of flight (t).
d = v0x * t
Substituting the values:
- d = 10.4 m/s * 0.763 seconds
Calculate the value, and we get:
- d ≈ 7.94 meters
Hence, the long jumper jumps approximately 7.94 meters.
To find out how far the long jumper will jump, we can use the equations of motion.
The horizontal distance traveled can be found by calculating the horizontal component of the velocity (Vx) and multiplying it by the time of flight.
Horizontal component of velocity (Vx) = initial velocity (11m/s) * cos(angle)
Let's calculate the horizontal component of velocity first:
Vx = 11m/s * cos(20°)
Vx = 11m/s * 0.9397
Vx = 10.3367 m/s
Now, we need to calculate the time of flight. We can use the vertical component of velocity (Vy), which is the initial velocity (11m/s) multiplied by the sine of the angle (20°).
Vertical component of velocity (Vy) = initial velocity (11m/s) * sin(angle)
Vy = 11m/s * sin(20°)
Vy = 11m/s * 0.3420
Vy = 3.7620 m/s
Since the jumper leaves the ground and lands at the same vertical position, we can use the vertical component of velocity (Vy) to calculate the total time of flight (T).
T = (2 * Vy) / g
Where g is the acceleration due to gravity, approximately 9.8 m/s^2.
T = (2 * 3.7620 m/s) / 9.8 m/s^2
T = 0.7680 s
Now, we can calculate the horizontal distance traveled (d) using the horizontal component of velocity (Vx) and the time of flight (T).
d = Vx * T
d = 10.3367 m/s * 0.7680 s
d = 7.933 m
Therefore, the long jumper will jump approximately 7.933 meters.