Problem 70.

Two cannonballs, A and B, are fired from the ground with identical initial speeds, but with launch angle of cannonball A larger than the launch angle of cannonball B.

(a) Which cannonball reaches a higher elevation?

(b) Which cannonball stays longer in the air?

(c) Which cannonball travels farther?

Solution:

(a) The vertical component of the initial velocity of the projectile is proportional to sinus of the launch angle. It means that the vertical component of initial velocity of cannonball A is larger than the vertical component of cannonball B. Then cannonball A reaches a higher elevation.

(b) The time in the air depends only on the vertical component of initial velocity of projectile. The larger the vertical component of the velocity the larger the time in the air. Then the cannonball A will stay longer in the air.

(c) From the data of the problem we cannot tell which one will travel farther. The horizontal length is proportional to . It has maximum at angle . Therefore we can have both possibilities:

cannonball A travels further than cannonball B (for example, if the launch angle of cannonball A is and the launch angler of cannonball B is ;

cannonball B travels further than cannonball A (for example, if the launch angle of cannonball B is and launch angler of cannonball A is ;