Win the Prize. In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of \(2.1 \mathrm{~m}\) from this point (Fig. E3.19). If you toss the coin with a velocity of \(6.4 \mathrm{~m} / \mathrm{s}\) at an angle of \(60^{\circ}\) above the horizontal, the coin lands in the dish. You can ignore air resistance. (a) What is the height of the shelf above the point where the quarter leaves your hand? (b) What is the vertical component of the velocity of the quarter just before it lands in the dish?
Step 1 of 2
Velocity of projection \(=6.4 \mathrm{~m} / \mathrm{s}\)
The \(\mathrm{x}\)-component of velocity \(=6.4 \times \cos 60^{\circ}\)
\(v_{x}=3.2 \mathrm{~m} / \mathrm{s}\)
The \(y\)-component of velocity \(=6.4 \times \sin 60^{\circ}\)
\(v_{y}=5.54 \mathrm{~m} / \mathrm{s}\)
Horizontal distance \(=2.1 \mathrm{~m}\)
Let, \(t\) be the time to cover this distance.
\(v_{x} t=2.1 \mathrm{~m}\)
\(t=2.1 / 3.2 \mathrm{~m} / \mathrm{s}\)
\(t=0.65 \mathrm{~s}\)
