Find the time tH it takes the projectile to reach its maximum height H. Express tH in terms of v0, θ, and g (the magnitude of the acceleration due to gravity).
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Find the time T it takes the projectile to reach its maximum height H. Express T in terms of v0, theta, and g (the magnitude of the acceleration due to gravity). Find tR, the time at which the projectile hits the ground after having traveled through a horizontal distance R. Express the time in terms of v0, theta, and g. Find H, the maximum height attained by the projectile. Express the time in terms of v0, theta, and g. Find the total distance R (often called the range) traveled in the x direction; see the figure in the problem introduction.
A projectile is fired with speed v0 at an angle from the horizontal as shown in the figure.
What is the highest point in the trajectory H in terms of acceleration due to gravity g, velocity v0, and angle θ? What is the range of the projectile R in terms of acceleration due to gravity g, velocity v0, and angle θ?
An artillery officer has the following problem. From his current position, he must shoot over a hill of height H at a target on the other side, which has the same elevation as his gun. He knows from his accurate map both the bearing and the distance R to the target and also that the hill is halfway to the target. To shoot as accurately as possible, he wants the projectile to just barely pass above the hill.
What is the angle in terms of H and R? What is the initial speed v0 in terms of g, R, and H? What is the flight time t of the projectile?
An arrow is fired with initial velocity v0 at an angle θ from the top of battlements, a height h above the ground. (a) In terms of h, v0, θ, and g, what is the time at which the arrow reaches its maximum height? (b) In terms of h, v0, θ, and g, what is the maximum height above the ground reached by the arrow?
