A cannon that is 10m long is designed to launch a 10kg ball over a castle wall.
In order to do this the ball must have a speed of at least 50m/s as it exits the
cannon. For every 10kg of explosives used, the force on the ball in the cannon
increases by 1000N. How many kg of explosives should they use?
A cannon that is 10m long is designed to launch a 10kg ball over a castle wall.
In order to do this the ball must have a speed of at least 50m/s as it exits the
cannon. For every 10kg of explosives used, the force on the ball in the cannon
increases by 1000N. How many kg of explosives should they use?
To determine the number of kilograms of explosives needed to launch the ball over the castle wall, we need to calculate the force required to achieve a speed of 50 m/s. We can then use this force to determine the amount of explosives needed based on the given increase in force for every 10 kg of explosives.
First, we need to determine the force required to achieve a speed of 50 m/s. We can use the equation of motion:
F = m * a
where F is the force, m is the mass, and a is the acceleration.
Since the ball is exiting a cannon, we can assume that the only force acting on it is due to the explosion. Therefore, the force acting on the ball is equal to the force exerted by the explosives.
Given that the mass of the ball is 10 kg and the desired velocity is 50 m/s, we can rearrange the equation to solve for force:
F = m * a
F = 10 kg * (50 m/s)^2
F = 10 kg * 2500 m^2/s^2
F = 25,000 N
So the minimum force required to launch the ball is 25,000 N.
Now, we can calculate the amount of explosives needed based on the increase in force for every 10 kg of explosives. From the given information, we know that every 10 kg of explosives increases the force by 1000 N.
To determine the number of kilograms of explosives needed, we divide the required force by the force increase per 10 kg of explosives:
Number of kg of explosives = Required force / Force increase per 10 kg of explosives
Number of kg of explosives = 25,000 N / 1000 N/10 kg
Number of kg of explosives = 25,000 N / 100 N/kg
Number of kg of explosives = 250 kg
Therefore, they should use 250 kg of explosives to launch the ball over the castle wall.