a projectile is launched straight up at 141 m/s. How fast is it moving at the top of its trajectory? suppose it is launched upward at 45 degree above the horizontal plane. how fast is it moving at the top of its curved trajectory?

The velocity of projectile has 2 components, horizontal component vcosθ and vertical component vsinθ, where v is the velocity of projection and θ is the angle between + ve X-axis and projectile motion.

In case 1, θ = 90⁰

So horizontal component is vcos90 = 0

Vertical component at maximum height = 0

So velocity at maximum height = 0 m/s

In case 2, θ = 45⁰

So horizontal component is 141cos45 = 100m/s

Vertical component at maximum height = 0

So velocity at maximum height = 100 m/s