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You are practicing throwing darts in your dorm. You stand 3.0 m from the wall on which the...

You are practicing throwing darts in your dorm. You stand 3.0 m from the wall on which the board hangs. the dart leaves your hand with a horizontal velocity at a point 2.0 m above the ground. The dart strikes the board at a point 1.65 m from the ground. Calculate:

a) the time of flight of the dart;

b) the initial speed of the dart;

c) the velocity of the dart when it hits the board.

Step-by-Step Solution

Solution 1
Step #1 of 13

SOLUTION:

THINK:

Horizontal distance,

Initial height,

Final height,

Acceleration due to gravity,

Step #2 of 13

RESEARCH:

(a)

Vertical displacement,

Here,

Initial velocity in vertical direction,

Acceleration,

Step #3 of 13

(b)

Initial velocity in horizontal direction = Final velocity in horizontal direction

Horizontal range,

Step #4 of 13

(c)

Vertical component of final velocity,

Magnitude of velocity on hitting the board,

Step #5 of 13

SIMPLIFY:

(a)

Vertical displacement,

Step #6 of 13

(b)

Initial velocity,

Step #7 of 13

(c)

Vertical component of final velocity,

Magnitude of velocity on hitting the board,

Step #8 of 13

CALCULATE:

(a)

Time of flight of the dart,

Step #9 of 13

(b)

Initial velocity of the dart,

Step #10 of 13
(c)

Magnitude of velocity on hitting the board:

Step #11 of 13

ROUND:

After rounding to two significant figures, we get

(a)

Time of flight of the dart,

Step #12 of 13

(b)

Initial velocity of the dart,

Step #13 of 13

(c)

Magnitude of velocity on hitting the board,

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