Question

# A projectile is launched at ground level with an

initial speed of 43.5 m/s at an angle of 35.0° above the horizontal. It strikes a target above the ground 3.40 seconds later. What are the *x* and *y* distances from where the projectile was launched to where it lands?

*x * distance m

*y* distance m

(A)

The cannon on a battleship can fire a shell a maximum distance of 44.9 km.

(B) Calculate the initial velocity of the shell in meters per second. (Enter the magnitude.)

m/s

What maximum height in meters does it reach? (At its highest, the shell is above a substantial part of the atmosphere—but air resistance is not really negligible as assumed to make this problem easier. Assume the shell has been fired so as to maximize horizontal distance.)

m

(C)

The ocean is not flat, because the earth is curved. Assume that the radius of the Earth is 6.37 **✕** 10^{3} km. How many meters lower will its surface be 44.9 km from the ship along a horizontal line parallel to the surface at the ship? m

(D)

Suppose you walk 20.2 m straight west and then 26.8 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements **A** and **B**, as in the figure below, then this problem asks you to find their sum **R** = **A** + **B**.)

Solve the problem above using analytical techniques, but reverse the order of the two legs of the walk. (This problem shows that adding them in reverse order gives the same result—that is, **B** + **A** = **A** + **B**. Enter the magnitude in m and the direction in degrees north of west.)

magnitude m direction ° north of west