please help! physics projectile question pt 2

Question

Spiff is thowing darts blindfolded. If he tosses the dart with an initial velocity vi = 19.1 m/s at an angle θ = 16 degrees above horizontal towards a wall that is d = 3.5 meters away. Find the distance Δy where the dart sticks into the wall measured up from the point of release. Make sure you do the following in your answer:
DO NOT include units. We'll deal with that in the next question.
Give precision to hundreths (#.##).
Make your answer correct to within 0.02

Answer 1

Using units helps to make sure the equations are correct.

 

The dart travels at 19.1 m/s for a distance of 3.5 m.  This takes 3.5 m / 19.1 m/s = .183 seconds.

Lets break the dart delta y into two parts.  The first is the dart velocity without gravity:

 

The 3.5 m to the wall is the bottom of a right triangle and the delta y is the opposite side from Spiff.

 

y = 3.5 tan 16 degrees = 3.5 * .2867 m = 1.004 m

 

Gravity is pulling the dart down at 9.8 m/s^2

 

y = 1/2 * 9.8 * .183^2 = 1/2 * 9.8 * .0336 m = .1645 m

 

The net delta y is 1.004 m - .1645 m = .839 m

 

Carl