An object is thrown into the air with a velocity of 30.0 m/s at an angle of 35.0° to
the horizontal. What is the range of this object?
To find the range of the object, we first need to determine the time it takes for the object to reach its maximum height.
The vertical component of the initial velocity is given by:
v = v₀ * sin(θ)
v = 30 * sin(35°)
v ≈ 17.20 m/s
Using the equation v = u + at, where v = 0 (since the object momentarily stops at the maximum height) and a = -9.8 m/s² (acceleration due to gravity):
0 = 17.20 - 9.8t
9.8t = 17.20
t ≈ 1.76 s
The time it takes to reach maximum height is approximately 1.76 seconds. The total time in the air will be double this time, so that the object will fall back to the same height from which it was thrown.
Therefore, the total time in the air is 2 * 1.76 = 3.52 seconds.
Now we can find the horizontal distance traveled by the object using the equation:
range = horizontal velocity * time
The horizontal component of the initial velocity is given by:
u = v₀ * cos(θ)
u = 30 * cos(35°)
u ≈ 24.53 m/s
range = 24.53 m/s * 3.52 s
range ≈ 86.24 meters
Therefore, the range of the object is approximately 86.24 meters.
To find the range of an object thrown into the air, we need to determine the horizontal distance traveled by the object.
The range (R) can be found using the formula:
R = (V^2 * sin(2θ)) / g
where:
V is the initial velocity (30.0 m/s)
θ is the launch angle (35.0°)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Let's plug in the given values and calculate the range:
R = (30.0^2 * sin(2 * 35.0°)) / 9.8
First, calculate the value inside the brackets:
2 * 35.0° = 70.0°
Next, calculate the sine of 70.0°:
sin(70.0°) ≈ 0.93969
Substitute this value back into the formula:
R ≈ (30.0^2 * 0.93969) / 9.8
R ≈ (900 * 0.93969) / 9.8
R ≈ 844.7211 / 9.8
R ≈ 86.23
Therefore, the approximate range of the object is 86.23 meters.
To find the range of an object in projectile motion, we need to know the initial velocity and launch angle. In this case, the initial velocity is 30.0 m/s and the launch angle is 35.0°.
The range is the horizontal distance traveled by the object before it hits the ground or comes back to the same level from where it was launched. In projectile motion, the range can be calculated using the following formula:
Range = (initial velocity^2 * sin(2*launch angle)) / gravitational acceleration
In this formula, the gravitational acceleration is usually considered as 9.8 m/s^2.
Now, let's calculate the range using the given values:
Range = (30.0 m/s)^2 * sin(2 * 35.0°) / 9.8 m/s^2
First, calculate the angle in radians:
2 * 35.0° = 70.0°
Convert to radians:
70.0° * (π / 180°) ≈ 1.2217 radians
Now, substitute the values into the formula:
Range = (900 m^2/s^2) * sin(1.2217) / 9.8 m/s^2
Calculate the value inside the sine function:
sin(1.2217) ≈ 0.9427
Substitute the value into the formula:
Range = (900 m^2/s^2) * 0.9427 / 9.8 m/s^2
Calculate the result:
Range ≈ 86.578 m
Therefore, the range of the object is approximately 86.578 meters.