Look at the equation for maximum height ,time of flight and range ,cheke the dimenation of each of these by putting them in to the eqution
To determine the dimensions of maximum height, time of flight, and range in an equation, you need to analyze the units of the variables involved. Let's consider the equations for these quantities:
1. Maximum Height (H):
The equation for maximum height in projectile motion can be expressed as:
H = (u² * sin²θ) / (2 * g)
where:
H is the maximum height,
u is the initial velocity,
θ is the launch angle, and
g is the acceleration due to gravity.
The units of the variables are as follows:
- u: velocity (m/s)
- θ: angle (radians or degrees)
- g: acceleration due to gravity (m/s²)
Now, let's analyze the dimensions of the equation:
[(m/s)² * sin²(angle)] / (m/s²) => m²/s²
Therefore, the dimension of maximum height (H) is meters (m).
2. Time of Flight (T):
The equation for time of flight can be expressed as:
T = (2 * u * sinθ) / g
where:
T is the time of flight (total time the projectile stays in the air),
u is the initial velocity,
θ is the launch angle, and
g is the acceleration due to gravity.
The units of the variables are as follows:
- u: velocity (m/s)
- θ: angle (radians or degrees)
- g: acceleration due to gravity (m/s²)
Now, let's analyze the dimensions of the equation:
[(m/s) * sin(angle)] / (m/s²) => s
Therefore, the dimension of time of flight (T) is seconds (s).
3. Range (R):
The equation for range can be expressed as:
R = (u² * sin2θ) / g
where:
R is the range (horizontal distance),
u is the initial velocity,
θ is the launch angle, and
g is the acceleration due to gravity.
The units of the variables are as follows:
- u: velocity (m/s)
- θ: angle (radians or degrees)
- g: acceleration due to gravity (m/s²)
Now, let's analyze the dimensions of the equation:
[(m/s)² * sin(2 * angle)] / (m/s²) => m
Therefore, the dimension of range (R) is meters (m).
By evaluating the variables and their corresponding units in the equations, you can determine the dimensions of maximum height, time of flight, and range.