A ball thrown vertically upward from ground is at height 80 m at two instants separated by 6 s. Initial speed is u=10x m/s. Find x; take g=10 m/s².
Physics · Mixed Chapter
JEE Main Practice

Question

A ball thrown vertically upward from ground is at height 80 m at two instants separated by 6 s. Initial speed is u=10x m/s. Find x; take g=10 m/s².

G1 Physics · Accepted Answer

Step 1: Height equation 80=ut−5t² gives quadratic 5t²−ut+80=0. Step 2: Its two roots are t₁,₂=[u∓√(u²−4×5×80)]/(2×5). Step 3: Difference Δt=t₂−t₁=√(u²−1600)/5. Set 6=√(u²−1600)/5⇒u²−1600=900⇒u=50 m/s. Step 4: Since u=10x, x=50/10=5.