Problem 86E

Projectile explorations A projectile launched from the ground with an initial speed of 20 m/s and a launch angle θ follow a trajectory approximated by

,

where x and y are the horizontal and vertical positions of the projectile relative to the launch point (0, 0).

a. Graph the trajectory for various values of θ in the range 0<θ<π/2.

b. Based on your observations, what value of θ gives the greatest range (the horizontal distance between the launch and landing points)?

Solution 86E

Given date

The trajectory of the projectile is given by

x = (20 cos) t, y = -4.9t2 + (20 sint, r

(b) by observing the above graph we can say that the maximum range occurs for