A baseball is thrown at an angle of 40.0 above the horizontal.The horizontal component of the baseball's initial velocity is 12.0 m/s^2 . What is the magnitude of the object's acceleration?
Your initial velocity cannot have dimentions of m/s^2
g is the answer, regardless of the angle, initial velocity or mass
To determine the magnitude of the object's acceleration, we need to break down the initial velocity into its horizontal and vertical components.
Given:
Initial velocity (v₀) = 12.0 m/s
Launch angle (θ) = 40.0°
The horizontal component of the initial velocity (v₀x) can be calculated using the formula:
v₀x = v₀ * cos(θ)
Substituting the given values into the formula:
v₀x = 12.0 m/s * cos(40.0°)
To evaluate this expression, use a scientific calculator or convert the angle to radians by multiplying it by π/180 and then find the cosine of the resulting angle.
Once you have the horizontal component of the velocity (v₀x), you can find the time it takes for the object to reach the highest point of its trajectory. Since there is no vertical acceleration at the highest point, the vertical component of the velocity (vᵥ) becomes zero.
Using the formula for the vertical component of velocity:
vᵥ = v₀ * sin(θ)
vᵥ = 12.0 m/s * sin(40.0°)
Again, evaluate this expression using a calculator or convert the angle to radians and find the sine of the resulting angle.
To find the time it takes to reach the highest point of the trajectory (t), divide the vertical component of velocity by the acceleration due to gravity (g).
Since the question doesn't provide the value of g, we can assume it to be approximately 9.8 m/s².
t = vᵥ / g
Now that you have time (t), you can calculate the vertical acceleration (aᵥ) using the formula:
aᵥ = -g
The negative sign indicates that the acceleration is directed downward.
Finally, to find the magnitude of the object's acceleration, you can use the formula:
a = sqrt((aₓ)² + (aᵥ)²)
where aₓ is the horizontal acceleration and aᵥ is the vertical acceleration. Since there is no horizontal acceleration in this case (the object follows a projectile motion), aₓ = 0.
Plugging the values into the equation:
a = sqrt((0)² + (-g)²)
Evaluate the expression by calculating -g (taking the acceleration due to gravity as a positive value) and taking the square root of the sum.
This will give you the magnitude of the object's acceleration.