Question

the equation above expresses the approximate height k, in meters, of a baseball above a baseball player t seconds after it is thrown vertically upward from the players hand with an initial velocity of 30 meters per second. how many seconds after the baseball is initially thrown, approximately, will it take for the baseball to return to the the player who threw the ball?
a 4.9
b 6
c 6.5
d 7
e 9

Explanation:

Step1: Set up the equation

When the baseball returns to the player, \( h = 0 \). So we set \( -4.9t^{2}+30t = 0 \).

Step2: Factor the equation

Factor out \( t \): \( t(-4.9t + 30)=0 \).

Step3: Solve for \( t \)

We have two solutions from \( t(-4.9t + 30)=0 \).

• First solution: \( t = 0 \) (this is the initial time when the ball is thrown).
• Second solution: Solve \( -4.9t+30 = 0 \).
• Add \( 4.9t \) to both sides: \( 30=4.9t \).
• Then \( t=\frac{30}{4.9}\approx6.12 \).

Since \( t = 0 \) is the start - time, we are interested in the non - zero solution. Among the given options, \( 6 \) is the closest to \( 6.12 \).

Answer:

B. 6