Problem 1

An object is launched from level ground with initial speed

v_0

at angle

\theta

above the horizontal. Neglect air resistance and take constant gravitational acceleration

g

. Find the flight time, range, and maximum height. Assume the string, pulley, electrical source, or optical apparatus is ideal as stated, and neglect any effect not specified. State a clear sign convention, identify the physical Keep one model and sign convention throughout. Reuse each intermediate result with the same convention, then check that the answer has the required physical dimensions. (a) Set up the physical relation. (b) Find an intermediate quantity. (c) Obtain the answer and check its conditions and units.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

v_y=0\Rightarrow t_{top}=v_0\sin\theta/g

problems.proof.analysis

At the apex vertical velocity vanishes, so the ascent time follows from $v_y=v_{0y}-gt$ . This is consistent with the stated model and the chosen sign convention.

problems.proof.pitfall. The apex condition is

v_y=0

, not zero total speed; horizontal velocity remains constant.