Problem 10
In a triangle ABC, if $\dfrac{2 \cos A}{a} + \dfrac{\cos B}{b} + \dfrac{2 \cos C}{c} = \dfrac{a}{bc} + \dfrac{b}{ca}$, find the value of angle $A$.
Problem 10
Given that $x + y + xy = 1$, where $x$ and $y$ are nonzero real numbers,find the value of $xy + \dfrac{1}{xy} - \dfrac{y}{x} - \dfrac{x}{y}$.
Problem 1011
A ship being launched slides down the ways with constant acceleration. She takes 8 sec to slide (the first foot | 0.3048 meter). How long will she take to slide down the ways if their length is (625 ft | 190.5 m)?
Problem 1010
A stone is thrown vertically up from the ground with a velocity of 300 ft per sec (91.44 m/s). How long must one wait before dropping a second stone from the top of a 600-ft (182.88-m) tower if the two stones are to pass each other 200 ft (60.96 m) from the top of the tower?
Problem 1009
A ball is shot vertically into the air at a velocity of 193.2 ft per sec (58.9 m per sec). After 4 sec, another ball is shot vertically into the air. What initial velocity must the second ball have in order to meet the first ball 386.4 ft (117.8 m) from the ground?
Problem 1019
The motion of a particle is given by the equation $s = 2t^4 - \frac{1}{6}t^3 + 2t^2$ where $s$ is in meter and $t$ in seconds. Compute the values of $v$ and $a$ when $t = 2 \, \text{ sec}$.
Problem 1008
A stone is thrown vertically upward from the ground with a velocity of 48.3 ft per sec (14.72 m per sec). One second later another stone is thrown vertically upward with a velocity of 96.6 ft per sec (29.44 m per sec). How far above the ground will the stones be at the same level?
Problem 1007
A stone is dropped from a captive balloon at an elevation of 1000 ft (304.8 m). Two seconds later another stone is thrown vertically upward from the ground with a velocity of 248 ft/s (75.6 m/s). If g = 32 ft/s2 (9.75 m/s2), when and where the stones pass each other?
Problem 1005
A stone is dropped down a well and 5 sec later, the sounds of the splash is heard. If the velocity of sound is 1120 ft/sec (341.376 m/s), what is the depth of the well?
Problem 1004
A ball is dropped from the top of a tower 80 ft (24.38 m) high at the same instant that a second ball is thrown upward from the ground with an initial velocity of 40 ft/sec (12.19 m/s). When and where do they pass, and with what relative velocity?
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