Integrated Concepts A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110 m. (a) Neglecting air resistance (a poor assumption, but we will make it for this example), calculate the shell’s velocity when it leaves the mortar. (b) The mortar itself is a tube 0.450 m long. Calculate the average acceleration of the shell in the tube as it goes from zero to the velocity found in (a). (c) What is the average force on the shell in the mortar? Express your answer in newtons and as a ratio to the weight of the shell.

Solution 47PE

We are required to calculate the velocity, acceleration and the average force on the shell under the given conditions.

Part a

Step 1 of 4</p>

The maximum height of the shell is given to be 110 m. At this height, the velocity is zero.

Let the initial velocity of the shell be .

From the kinematic equation,

m/s

m/s

The shell has a velocity of 46.4 m/s while it leaves the mortar.

Part b

Step 2 of 4</p>

Here, the initial velocity of the shell is zero.

It reaches a velocity of 46.4 m/s.

Length of the mortar tube 0.450 m.

From the kinematic equation,

m/s2

The shell has an average acceleration of 2392 m/s2.

Part c