State the dimensions of acceleration, pressure, and density. Calculate the maximum height of a projectile launched with initial velocity 42 m/s at 30 degrees, with a time of flight of 4.2 s and g = 10

Here are the solutions to the questions:

1. State the dimensions of the following physical quantities:

• a) acceleration Acceleration is the rate of change of velocity. Velocity has dimensions of length (L) divided by time (T).

  $$\text{Dimension of velocity} = \frac{\text{L}}{\text{T}} = \text{LT}^{-1}$$

  Acceleration is velocity divided by time.

  $$\text{Dimension of acceleration} = \frac{\text{LT}^{-1}}{\text{T}} = \boxed{\text{LT}^{-2}}$$

• b) pressure Pressure is force per unit area. Force has dimensions of mass (M) times acceleration (LT$^{-2}$).

  $$\text{Dimension of force} = \text{M} \times \text{LT}^{-2} = \text{MLT}^{-2}$$

  Area has dimensions of length squared (L$^2$).

  $$\text{Dimension of pressure} = \frac{\text{MLT}^{-2}}{\text{L}^2} = \boxed{\text{ML}^{-1}\text{T}^{-2}}$$

• c) density Density is mass per unit volume. Volume has dimensions of length cubed (L$^3$).

  $$\text{Dimension of density} = \frac{\text{M}}{\text{L}^3} = \boxed{\text{ML}^{-3}}$$

2. A projectile is launched with a velocity of $42 \, \text{m/s}$ at an angle of $30^\circ$ to the horizontal. If the time of flight is $4.2 \, \text{s}$, calculate the maximum attainable height. $|g = 10 \, \text{m/s}^2|$

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