A water balloon is launched at a building 24m away with an initial velocity of 18 m/s at an angle of 50° above the horizontal. If the balloon misses or shoots over the building, how far will the balloon land from its launch location?
12ms
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To find out how far the balloon will land from its launch location, we need to analyze its trajectory and determine the horizontal distance it travels.
We can start by breaking down the initial velocity into its horizontal and vertical components. The horizontal component can be calculated using the formula:
Vx = V * cos(θ)
Where:
Vx is the horizontal component of the velocity
V is the initial velocity of the balloon
θ is the launch angle
Substituting the given values:
Vx = 18 m/s * cos(50°)
Calculating Vx:
Vx = 18 m/s * 0.64279
Vx ≈ 11.570 m/s
Now, we can determine the time it takes for the balloon to reach the building. To calculate this, we can use the formula for horizontal motion:
D = Vx * t
Where:
D is the horizontal distance
Vx is the horizontal component of the velocity
t is the time of flight
Substituting the given values:
24 m = 11.570 m/s * t
Simplifying:
t = 24 m / 11.570 m/s
t ≈ 2.073 s
Now that we know the time of flight, we can calculate the vertical distance the balloon travels using the formula for vertical motion:
Vy = V * sin(θ)
Where:
Vy is the vertical component of the velocity
V is the initial velocity of the balloon
θ is the launch angle
Substituting the given values:
Vy = 18 m/s * sin(50°)
Calculating Vy:
Vy = 18 m/s * 0.76604
Vy ≈ 13.789 m/s
Using the formula for vertical motion:
h = Vy * t + (0.5 * g * t^2)
Where:
h is the vertical distance
Vy is the vertical component of the velocity
t is the time of flight
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Substituting the values:
h = 13.789 m/s * 2.073 s + 0.5 * 9.8 m/s^2 * (2.073 s)^2
Calculating h:
h = 28.605 m + 21.934 m
h ≈ 50.539 m
Therefore, the balloon will land approximately 50.539 meters above the launch location if it misses or shoots over the building.
To determine how far the water balloon will land from its launch location, we can use the equations of projectile motion.
First, let's break down the initial velocity into its horizontal and vertical components. The horizontal component (Vx) can be found by multiplying the initial velocity (18 m/s) by the cosine of the launch angle (50°):
Vx = 18 m/s × cos(50°)
Next, we can calculate the time of flight of the water balloon, which is the total time it takes for the projectile to hit the ground. Since we are only interested in the horizontal motion, we can use the following equation:
Time of flight = 2 × (Vertical component of initial velocity) / acceleration due to gravity
The vertical component of the initial velocity (Vy) can be found by multiplying the initial velocity (18 m/s) by the sine of the launch angle (50°):
Vy = 18 m/s × sin(50°)
Acceleration due to gravity is approximately 9.8 m/s².
Now, we can substitute the values into the equation to calculate the time of flight:
Time of flight = 2 × Vy / g
where g is the acceleration due to gravity.
Once we have the time of flight, we can find the horizontal distance traveled (range) using the equation:
Range = Vx × Time of flight
By substituting the values and solving these equations, we can determine the range at which the water balloon lands from its launch location.