A cannon tilted upward at 30° fires a cannonball with a speed of 100 m/s. What is the component of the cannonball's velocity parallel to the ground?

Ruth sets out to visit her friend Ward, who lives 50 mi north and 100 mi east of her. She starts by driving east, but after 30 mi she comes to a detour that takes her 15 mi south before going east again. She then drives east for 8 mi and runs out of gas, so Ward flies there in his small plane to get her. What is Ward's displacement vector? Give your answer (a) in component form, using a coordinate system in which the y-axis points north, and (b) as a magnitude and direction.

While vacationing in the mountains you do some hiking. In the morning, your displacement is $\(\mathbf{S}\)_{morning} = (2000 \, \(\text{m}\), \(\text{east}\)) + (3000 \, \(\text{m}\), \(\text{north}\)) + (200 \, \(\text{m}\), \(\text{vertical}\))$. Continuing on after lunch, your displacement is $\(\mathbf{S}\)_{afternoon} = (1500 \, \(\text{m}\), \(\text{west}\)) + (2000 \, \(\text{m}\), \(\text{north}\)) - (300 \, \(\text{m}\), \(\text{vertical}\))$. What is the magnitude of your net displacement for the day?

Jack and Jill ran up the hill at 3.0 m/s. The horizontal component of Jill's velocity vector was 2.5 m/s. What was the angle of the hill?

A cannonball leaves the barrel with velocity v = (75î ＋ 45ĵ). At what angle is the barrel tilted above horizontal?

Trevon drives with velocity v₁ = (55î - 10ĵ) mph for 1.0 h, then v₂ = (20î ＋ 50ĵ) mph for 2.0 h. What is Trevon's displacement? Write your answer in component form using unit vectors.

You are fixing the roof of your house when a hammer breaks loose and slides down. The roof makes an angle of 35° with the horizontal, and the hammer is moving at 4.5 m/s when it reaches the edge. What are the horizontal and vertical components of the hammer's velocity just as it leaves the roof?